{"product_id":"the-mazya-anniversary-collection-jrgen-rossmann-9783764362010","title":"The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's Work in Functional Analysis, Partial Differential Equations and Applications","description":"Vladimir Maz'ya: Friend and mathematician. Recollections.- On Maz'ya's work in potential theory and the theory of function spaces.- 1. Introduction.- 2. Embeddings and isoperimetric inequalities.- 3. Regularity of solutions.- 4. Boundary regularity.- 5. Nonlinear potential theory.- Maz'ya's works in the linear theory of water waves.- 1. Introduction.- 2. The unique solvability of the water wave problem.- 3. The Neumann-Kelvin problem.- 4. Asymptotic expansions for transient water waves due to brief and high-frequency disturbances.- Maz'ya's work on integral and pseudodifferential operators.- 1. Non-elliptic operators.- 2. Oblique derivative problem: breakthrough in the generic case of degeneration.- 3. Estimates for differential operators in the half-space.- 4. The characteristic Cauchy problem for hyperbolic equations.- 5. New methods for solving ill-posed boundary value problems.- 6. Applications of multiplier theory to integral operators.- 7. Integral equations of harmonic potential theory on general non-regular surfaces.- 8. Boundary integral equations on piecewise smooth surfaces.- Contributions of V. Maz'ya to the theory of boundary value problems in nonsmooth domains.- 1. Maz'ya's early work on boundary value problems in nonsmooth domains.- 2. General elliptic boundary value problems in domains with point singularities.- 3. Boundary value problems in domains with edges.- 4. Spectral properties of operator pencils generated by elliptic boundary value problems in a cone.- 5. Applications to elastostatics and hydrodynamics.- 6. Singularities of solutions to nonlinear elliptic equations at a cone vertex.- On some potential theoretic themes in function theory.- 1. Approximation theory.- 2. Uniqueness properties of analytic functions.- 3. The Cauchy problem for the Laplace equation.- Approximate approximations and their applications.- 1. Introduction.- 2. Quasi-interpolation.- 3. Generating functions for quasi-interpolation of high order.- 4. Semi-analytic cubature formulas.- 5. Cubature of integral operators over bounded domains.- 6. Approximate wavelets.- 7. Numerical algorithms based upon approximate approximations.- Maz'ya's work on the biography of Hadamard.- Isoperimetric inequalities and capacities on Riemannian manifolds.- 1. Introduction.- 2. Capacity of balls.- 3. Parabolicity of manifolds.- 4. Isoperimetric inequality and Sobolev inequality.- 5. Capacity and the principal frequency.- 6. Cheeger's inequality.- 7. Eigenvalues of balls on spherically symmetric manifolds.- 8. Heat kernel on spherically symmetric manifolds.- Multipliers of differentiable functions and their traces.- 1. Introduction.- 2. Description and properties of multipliers.- 3. Multipliers in the space of Bessel potentials as traces of multipliers.- An asymptotic theory of nonlinear abstract higher order ordinary differential equations.- Sobolev spaces for domains with cusps.- 1. Introduction.- 2. Extension theorems.- 3. Embedding theorems.- 4. Boundary values of Sobolev functions.- Extension theorems for Sobolev spaces.- 1. Introduction.- 2. Extensions with preservation of class.- 3. Estimates for the minimal norm of an extension operator.- 4. Extensions with deterioration of class.- Contributions of V.G. Maz'ya to analysis of singularly perturbed boundary value problems.- 1. Introduction.- 2. Domain with a small hole.- 3. General asymptotic theory by Maz'ya, Nazarov and Plamenevskii.- 4. Asymptotics of solutions of boundary integral equations under a small perturbation of a corner.- 5. Compound asymptotics for homogenization problems.- 6. Boundary value problems in 3D-1D multi-structures.- Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain.- 1. Introduction.- 2. Formulation of the problem.- 3. The leading order approximation.- A history of the Cosserat spectrum.- 1. Introduction.- 2. The first boundary value problem of elastostatics.- 3. The second and other boundary-value problems.- 4. Applications and o...\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e J]rgen Rossmann\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3764362014\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783764362010\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/18\/1999\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 380\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.77lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.88d","brand":"J]rgen Rossmann","offers":[{"title":"Hardcover","offer_id":48136987312383,"sku":"9783764362010","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_bbf1172b-6b04-4fa0-b1be-fa242ad76f3e.jpg?v=1770165789","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-mazya-anniversary-collection-jrgen-rossmann-9783764362010","provider":"WR Book House","version":"1.0","type":"link"}