Ebook: The Maz’ya Anniversary Collection: Volume 1: On Maz’ya’s work in functional analysis, partial differential equations and applications

The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par­ tially based on talks given at the conference "Functional Analysis, Partial Differ­ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the­ ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.

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This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.

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This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.
Content:
Front Matter....Pages i-xii
Vladimir Maz’ya: Friend and mathematician. Recollections....Pages 1-5
On Maz’ya’s work in potential theory and the theory of function spaces....Pages 7-16
Maz’ya’s works in the linear theory of water waves....Pages 17-34
The work of Vladimir Maz’ya on integral and pseudodifferential operators....Pages 35-52
Contributions of V. Maz’ya to the theory of boundary value problems in nonsmooth domains....Pages 53-98
On some potential theoretic themes in function theory....Pages 99-110
Approximate Approximations and their Applications....Pages 111-136
Maz’ya’s work on the biography of Hadamard....Pages 137-138
Isoperimetric inequalities and capacities on Riemannian manifolds....Pages 139-153
Multipliers of differentiable functions and their traces....Pages 155-169
An asymptotic theory of nonlinear abstract higher order ordinary differential equations....Pages 171-173
Sobolev spaces for domains with cusps....Pages 175-185
Extension theorems for Sobolev spaces....Pages 187-200
Contributions of V.G. Maz’ya to analysis of singularly perturbed boundary value problems....Pages 201-212
Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain....Pages 213-221
A history of the Cosserat spectrum....Pages 223-234
Boundary integral equations on a contour with cusp....Pages 235-242
On Maz’ya type inequalities for convolution operators....Pages 243-248
Sharp constants and maximum principles for elliptic and parabolic systems with continuous boundary data....Pages 249-306
L p -contractivity of semigroups generated by parabolic matrix differential operators....Pages 307-330
Back Matter....Pages 331-364

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This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.
Content:
Front Matter....Pages i-xii
Vladimir Maz’ya: Friend and mathematician. Recollections....Pages 1-5
On Maz’ya’s work in potential theory and the theory of function spaces....Pages 7-16
Maz’ya’s works in the linear theory of water waves....Pages 17-34
The work of Vladimir Maz’ya on integral and pseudodifferential operators....Pages 35-52
Contributions of V. Maz’ya to the theory of boundary value problems in nonsmooth domains....Pages 53-98
On some potential theoretic themes in function theory....Pages 99-110
Approximate Approximations and their Applications....Pages 111-136
Maz’ya’s work on the biography of Hadamard....Pages 137-138
Isoperimetric inequalities and capacities on Riemannian manifolds....Pages 139-153
Multipliers of differentiable functions and their traces....Pages 155-169
An asymptotic theory of nonlinear abstract higher order ordinary differential equations....Pages 171-173
Sobolev spaces for domains with cusps....Pages 175-185
Extension theorems for Sobolev spaces....Pages 187-200
Contributions of V.G. Maz’ya to analysis of singularly perturbed boundary value problems....Pages 201-212
Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain....Pages 213-221
A history of the Cosserat spectrum....Pages 223-234
Boundary integral equations on a contour with cusp....Pages 235-242
On Maz’ya type inequalities for convolution operators....Pages 243-248
Sharp constants and maximum principles for elliptic and parabolic systems with continuous boundary data....Pages 249-306
L p -contractivity of semigroups generated by parabolic matrix differential operators....Pages 307-330
Back Matter....Pages 331-364
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