The Dirichlet problem with L²-boundary data for elliptic linear equations
by Jan Chabrowski
The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.
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Differential equations, Elliptic, Dirichlet problem, Elliptic Differential equations, Numerical solutions, Probleem van Dirichlet, Dirichlet, Problème de, Elliptische differentiaalvergelijkingen, Solutions numériques, Équation linéaire, EDP, Équation elliptique, Problème Dirichlet, Équations différentielles elliptiques, Résolution équation, Forms (mathematics), Differential equations, numerical solutions, Mathematics, Potential theory (Mathematics), Potential Theory| Edition | Availability |
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The Dirichlet problem with L²-boundary data for elliptic linear equations
1991, Springer-Verlag
in English
3540544860 9783540544869
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Includes bibliographical references (p. 168-171) and index.
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- Created April 1, 2008
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| March 28, 2025 | Edited by ImportBot | Redacting ocaids |
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