Sobolev Spaces in Mathematics I
This volume is dedicated to the centenary of the outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated work On a theorem of functional analysis, published in 1938, exactly 70 years ago, was where the original Sobolev inequality was proved. This double event is a good occasion to gather experts for presenting the latest results on the study of Sobolev inequalities, which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev-type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc.
The volume opens with a nice survey reminiscence, My Love Affair with the Sobolev Inequality, by David R. Adams.
Presentation of new results on the latest topics of the theory Sobolev spaces, partial differential equations, analysis and mathematical physicsThe authors and editors are world-known specialists, working in different countriesPublication on the centenary of Sobolev’s birth with two short biographical articles and unique archive photos of S. Sobolev which have not been published earlier in the English-language literature