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Besov regularity for elliptic boundary value problems

Besov regularity for elliptic boundary value problems This paper studies the regularity of solutions to boundary value problems for the Laplace operator on Lipschitz domains R in Rd and its relationship with adaptive and other nonlinear methods for approxi- mating these solutions. The smoothness spaces which determine the ef- ficiency of such nonlinear approximation in L,(O) are the Besov spaces B,"(L7(0)), T := (c~ld + l/p)-l. Thus, the regularity of the solution in this scale of Besov spaces is investigated with the aim of determining the largest a for which the solution is in B:(L,(R)). The regularity the- orems given in this paper build upon the recent results of Jerison and Kenig [lo]. The proof of the regularity theorem uses characterizations of Besov spaces by wavelet expansions. Key Words: Besov spaces, elliptic boundary value problems, potential theory, adaptive methods, nonlinear approximation, wavelets AMS Subject classification: primary 35B65, secondary 31B10, 41.446, 16E35, 65N30 h he work of this author has been supported by Deutsche Forschungsgemeinschaft (Da 36011-1) 'The work of th~s author has been supported by the Office of Naval Research Contract N0014-91-J1343. Copyright t'C3 1997 by Marcel Dekker, Inc DAHLKE AND DEVORE 1 Introduction This paper is concerned with the regularity of solutions to second order http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Partial Differential Equations Taylor & Francis

Besov regularity for elliptic boundary value problems

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References (9)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1532-4133
eISSN
0360-5302
DOI
10.1080/03605309708821252
Publisher site
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Abstract

This paper studies the regularity of solutions to boundary value problems for the Laplace operator on Lipschitz domains R in Rd and its relationship with adaptive and other nonlinear methods for approxi- mating these solutions. The smoothness spaces which determine the ef- ficiency of such nonlinear approximation in L,(O) are the Besov spaces B,"(L7(0)), T := (c~ld + l/p)-l. Thus, the regularity of the solution in this scale of Besov spaces is investigated with the aim of determining the largest a for which the solution is in B:(L,(R)). The regularity the- orems given in this paper build upon the recent results of Jerison and Kenig [lo]. The proof of the regularity theorem uses characterizations of Besov spaces by wavelet expansions. Key Words: Besov spaces, elliptic boundary value problems, potential theory, adaptive methods, nonlinear approximation, wavelets AMS Subject classification: primary 35B65, secondary 31B10, 41.446, 16E35, 65N30 h he work of this author has been supported by Deutsche Forschungsgemeinschaft (Da 36011-1) 'The work of th~s author has been supported by the Office of Naval Research Contract N0014-91-J1343. Copyright t'C3 1997 by Marcel Dekker, Inc DAHLKE AND DEVORE 1 Introduction This paper is concerned with the regularity of solutions to second order

Journal

Communications in Partial Differential Equations – Taylor & Francis

Published: Jan 1, 1997

Keywords: Besov spaces; elliptic boundary; value problemspotential theory; adaptive methods; nonlinear approximation; wavelets

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