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Research articles and surveys from world-recognized mathematicians cover large areas in Analysis where the contributions of Prof. Maz'ya are fundamental, influential, and/or pioneering. Among more than 25 monographs and 450 research papers by V. Maz'ya, one can find deep results predetermining the further development of very diverse topics, which is reflected in the collected papers. Recent advantages in the theory of Sobolev spaces are presented. Hardy-Sobolev-Maz'ya inequalities, Maz'ya isocapacitary inequalities, isoperimetric inequalities, sharp constants, extension operators are generalized in various settings. Important PDEs are studied by methods of homogenization, multiscale expansion, matched asymptotic expansions, etc. Various problems in Analysis, like Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems and many other problems are treated.
Archive photos representative, in particular, meetings of V. Maz'ya with S. Sobolev and with L. Schwarz are included. List of references to Maz'ya's works throughout the volumes companions the collection.
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