03238nam 2200625 450 99646675920331620220305043210.03-540-38400-610.1007/BFb0095750(CKB)1000000000437081(SSID)ssj0000322651(PQKBManifestationID)12099109(PQKBTitleCode)TC0000322651(PQKBWorkID)10289053(PQKB)10448749(DE-He213)978-3-540-38400-7(MiAaPQ)EBC5577525(Au-PeEL)EBL5577525(OCoLC)1066193715(MiAaPQ)EBC6842502(Au-PeEL)EBL6842502(OCoLC)1292359513(PPN)155169394(EXLCZ)99100000000043708120220305d1991 uy 0engurnn#008mamaatxtccrThe Dirichlet problem with Lp-boundary data for elliptic linear equations /Jan Chabrowski1st ed. 1991.Berlin, Heidelberg :Springer-Verlag,[1991]©19911 online resource (VI, 173 p.)Lecture Notes in Mathematics ;1482Bibliographic Level Mode of Issuance: Monograph0-387-54486-0 3-540-54486-0 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.Lecture notes in mathematics (Springer-Verlag) ;1482.Dirichlet problemDifferential equations, EllipticNumerical solutionsDirichlet problem.Differential equations, EllipticNumerical solutions.517Chabrowski Jan1941-59970MiAaPQMiAaPQMiAaPQBOOK996466759203316The Dirichlet problem with Lp-boundary data for elliptic linear equations2831033UNISA