Carleman Estimates Observability Inequalities And Null Controllability For Interior Degenerate Nonsmooth Parabolic Equations

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Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations

Genni Fragnelli,Dimitri Mugnai
Carleman Estimates Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations Book PDF

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 48,6 Mb
Release : 2016-06-21
Category : Carleman theorem
ISBN : 9781470419547

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Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations by Genni Fragnelli,Dimitri Mugnai Pdf

The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences

Genni Fragnelli,Dimitri Mugnai
Corrigendum and Improvements to Carleman Estimates Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and Its Consequences Book PDF

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : American Mathematical Society
Page : 19 pages
File Size : 54,9 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9781470447878

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Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences by Genni Fragnelli,Dimitri Mugnai Pdf

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Control of Degenerate and Singular Parabolic Equations

Genni Fragnelli,Dimitri Mugnai
Control of Degenerate and Singular Parabolic Equations Book PDF

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : Springer Nature
Page : 105 pages
File Size : 42,7 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9783030693497

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Control of Degenerate and Singular Parabolic Equations by Genni Fragnelli,Dimitri Mugnai Pdf

This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

Carleman Estimates for Second Order Partial Differential Operators and Applications

Xiaoyu Fu,Qi Lü,Xu Zhang
Carleman Estimates for Second Order Partial Differential Operators and Applications Book PDF

Author : Xiaoyu Fu,Qi Lü,Xu Zhang
Publisher : Springer Nature
Page : 127 pages
File Size : 49,9 Mb
Release : 2019-10-31
Category : Mathematics
ISBN : 9783030295301

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Carleman Estimates for Second Order Partial Differential Operators and Applications by Xiaoyu Fu,Qi Lü,Xu Zhang Pdf

This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.

$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

Steve Hofmann,Dorina Mitrea,Marius Mitrea
L p Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets Book PDF

Author : Steve Hofmann,Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 44,8 Mb
Release : 2017-01-18
Category : Function spaces
ISBN : 9781470422608

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$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by Steve Hofmann,Dorina Mitrea,Marius Mitrea Pdf

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Ariel Barton:,Svitlana Mayboroda
Layer Potentials and Boundary Value Problems for Second Order Elliptic Operators with Data in Besov Spaces Book PDF

Author : Ariel Barton:,Svitlana Mayboroda
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 43,8 Mb
Release : 2016-09-06
Category : Besov space
ISBN : 9781470419899

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Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces by Ariel Barton:,Svitlana Mayboroda Pdf

This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation

Hans Lundmark,Jacek Szmigielski
An Inverse Spectral Problem Related to the Geng Xue Two Component Peakon Equation Book PDF

Author : Hans Lundmark,Jacek Szmigielski
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 46,5 Mb
Release : 2016-10-05
Category : Discontinuous functions
ISBN : 9781470420260

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An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation by Hans Lundmark,Jacek Szmigielski Pdf

The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ``discrete cubic string'' type-a nonselfadjoint generalization of a classical inhomogeneous string--but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type, implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string.

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

Reiner Hermann:
Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology Book PDF

Author : Reiner Hermann:
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 51,5 Mb
Release : 2016-09-06
Category : Associative rings
ISBN : 9781470419950

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Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology by Reiner Hermann: Pdf

In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Descent Construction for GSpin Groups

Joseph Hundley,Eitan Sayag
Descent Construction for GSpin Groups Book PDF

Author : Joseph Hundley,Eitan Sayag
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 46,9 Mb
Release : 2016-09-06
Category : Descent
ISBN : 9781470416676

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Descent Construction for GSpin Groups by Joseph Hundley,Eitan Sayag Pdf

In this paper the authors provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is, representations which are isomorphic to the twist of their own contragredient by some Hecke character. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n.

Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting

J. P. Pridham
Real Non Abelian Mixed Hodge Structures for Quasi Projective Varieties Formality and Splitting Book PDF

Author : J. P. Pridham
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 45,9 Mb
Release : 2016-09-06
Category : Hodge theory
ISBN : 9781470419813

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Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting by J. P. Pridham Pdf

The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x−i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.

Abelian Properties of Anick Spaces

Brayton Gray
Abelian Properties of Anick Spaces Book PDF

Author : Brayton Gray
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 53,7 Mb
Release : 2017-02-20
Category : Abelian groups
ISBN : 9781470423087

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Abelian Properties of Anick Spaces by Brayton Gray Pdf

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

Proof of the 1-Factorization and Hamilton Decomposition Conjectures

Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Proof of the 1 Factorization and Hamilton Decomposition Conjectures Book PDF

Author : Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 53,6 Mb
Release : 2016-10-05
Category : 1-factorization
ISBN : 9781470420253

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown Pdf

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

The $abc$-Problem for Gabor Systems

Xin-Rong Dai,Qiyu Sun
The abc Problem for Gabor Systems Book PDF

Author : Xin-Rong Dai,Qiyu Sun
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 40,7 Mb
Release : 2016-10-05
Category : Gabor frames
ISBN : 9781470420154

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The $abc$-Problem for Gabor Systems by Xin-Rong Dai,Qiyu Sun Pdf

A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.

Semicrossed Products of Operator Algebras by Semigroups

Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Semicrossed Products of Operator Algebras by Semigroups Book PDF

Author : Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 55,9 Mb
Release : 2017-04-25
Category : Operator algebras
ISBN : 9781470423094

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Semicrossed Products of Operator Algebras by Semigroups by Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis Pdf

The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Intersection Local Times, Loop Soups and Permanental Wick Powers

Yves Le Jan,Michael B. Marcus,Jay Rosen
Intersection Local Times Loop Soups and Permanental Wick Powers Book PDF

Author : Yves Le Jan,Michael B. Marcus,Jay Rosen
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 52,9 Mb
Release : 2017-04-25
Category : Gaussian processes
ISBN : 9781470436957

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Intersection Local Times, Loop Soups and Permanental Wick Powers by Yves Le Jan,Michael B. Marcus,Jay Rosen Pdf

Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.