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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Sobolev Spaces in Mathematics III - Applications in Mathematical Physics (Paperback, Softcover reprint of hardcover 1st ed. 2009)
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Sobolev Spaces in Mathematics III - Applications in Mathematical Physics (Paperback, Softcover reprint of hardcover 1st ed. 2009)
Series: International Mathematical Series, 10
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Victor Isakov This volume contains various results on partial
di?erential equations where Sobolev spaces are used. Their
selection is motivated by the research int- ests of the editor and
the geographicallinks to the places where S. L. Sobolev worked and
lived: St. Petersburg, Moscow, and Novosibirsk. Most of the papers
are written by leading experts in control theory and inverse pr-
lems. Another reason for the selection is a strong link to applied
areas. In my opinion, control theory and inverse problems are main
areas of di?er- tial equations of importance for some branches of
contemporary science and engineering. S. L. Sobolev, as many great
mathematicians, was very much motivated by applications. He did not
distinguished between pure and - plied mathematics, but, in his own
words, between "good mathematics and bad mathematics. " While he
possessed a brilliant analytical technique, he most valued
innovative ideas, solutions of deep conceptual problems, and not
mathematical decorations, perfecting exposition, and
"generalizations. " S. L. Sobolev himself never published papers on
inverse problems or c- trol theory, but he was very much aware of
the state of art and he monitored research on inverse problems. In
particular, in his lecture at a Conference on
Di?erentialEquationsin1954(found inSobolev'sarchiveandmadeavailable
to me by Alexander Bukhgeim), he outlined main inverse problems in
g- physics: theinverseseismicproblem,
theelectromagneticprospecting, andthe inverse problem of
gravimetry.
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