A remark on the Sobolev regularity of classical solutions of strongly elliptic equations

Journal article

Authors/Editors

Milani, Albert

Research Areas

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Publication Details

Author list: Milani A

Publisher: WILEY-V C H VERLAG GMBH

Place: BERLIN

Publication year: 1998

Journal acronym: MATH NACHR

Volume number: 190

Start page: 203

End page: 219

Number of pages: 17

ISSN: 0025-584X

Languages: English-Great Britain (EN-GB)

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Abstract

We prove that C-2,C-alpha(<(Omega)over bar>) solutions of problem (1.2) below are in Hm+2(Omega) for all m is an element of IN, if f and the coefficients are in H-m(Omega) boolean AND C-0,C-alpha(<(Omega)over bar>). Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11) below.

Keywords

elliptic estimates, regularity

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