Sobolev spaces become the established and universal language of
partial differential equations and mathematical analysis. Among a
huge variety of problems where Sobolev spaces are used, the
following important topics are the focus of this volume: boundary
value problems in domains with singularities, higher order partial
differential equations, local polynomial approximations,
inequalities in Sobolev-Lorentz spaces, function spaces in cellular
domains, the spectrum of a Schrodinger operator with negative
potential and other spectral problems, criteria for the complete
integration of systems of differential equations with applications
to differential geometry, some aspects of differential forms on
Riemannian manifolds related to Sobolev inequalities, Brownian
motion on a Cartan-Hadamard manifold, etc.
Two short biographical articles on the works of Sobolev in the
1930s and the foundation of Akademgorodok in Siberia, supplied with
unique archive photos of S. Sobolev are included.
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