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Catalogue Information
Field name	Details
Dewey Class	515
Title	The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations ([EBook]) / by Jan Chabrowski.
Author	Chabrowski, Jan. , 1941-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1991.
Physical Details	VI, 173 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1482
ISBN	9783540384007
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0095750
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Fourier Analysis . Mathematical analysis . Mathematics . Potential Theory . Potential theory (Mathematics) . Authors: Chabrowski, Jan. 1941- . Chabrowski, Jan, 1941- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515 .

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The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations

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