The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations
Chabrowski, Jan.
The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations [electronic resource] / by Jan Chabrowski. - VI, 173 p. online resource. - Lecture Notes in Mathematics, 1482 0075-8434 ; . - Lecture Notes in Mathematics, 1482 .
Weighted Sobolev space -- The Dirichlet problem in a half-space -- The Dirichlet problem in a bounded domain -- Estimates of derivatives -- Harmonic measure -- Exceptional sets on the boundary -- Applications of the L 2-method -- Domains with C1,?-boundary -- The space C n?1( ) -- C n?1-estimate of the solution of the Dirichlet problem with L 2-boundary data.
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.
9783540384007
10.1007/BFb0095750 doi
Global analysis (Mathematics).
Potential theory (Mathematics).
Fourier analysis.
Analysis.
Potential Theory.
Fourier Analysis.
QA299.6-433
515
The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations [electronic resource] / by Jan Chabrowski. - VI, 173 p. online resource. - Lecture Notes in Mathematics, 1482 0075-8434 ; . - Lecture Notes in Mathematics, 1482 .
Weighted Sobolev space -- The Dirichlet problem in a half-space -- The Dirichlet problem in a bounded domain -- Estimates of derivatives -- Harmonic measure -- Exceptional sets on the boundary -- Applications of the L 2-method -- Domains with C1,?-boundary -- The space C n?1( ) -- C n?1-estimate of the solution of the Dirichlet problem with L 2-boundary data.
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.
9783540384007
10.1007/BFb0095750 doi
Global analysis (Mathematics).
Potential theory (Mathematics).
Fourier analysis.
Analysis.
Potential Theory.
Fourier Analysis.
QA299.6-433
515