โ Scribed by Vladimir Maz'ya, Vladimir Maz'ya
No coin nor oath required. For personal study only.
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.
๐ SIMILAR VOLUMES
Partial Differential Equations (pdes) Are Fundamental To The Modeling Of Natural Phenomena, Arising In Every Field Of Science. Consequently, The Desire To Understand The Solutions Of These Equations Has Always Had A Prominent Place In The Efforts Of Mathematicians; It Has Inspired Such Diverse Field
This book offers an ideal graduate-level introduction to the theory of partial differential equations.ย The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections