Besov regularity for elliptic boundary value problems Academic Article

abstract

• This paper studies the regularity of solutions to boundary value problems for the Laplace operator on Lipschitz domains in Rd and its relationship with adaptive and other nonlinear methods for approximating these solutions. The smoothness spaces which determine the efficiency of such nonlinear approximation in Lp() are the Besov spaces B (L()), := (/d + 1/p)-1. Thus, the regularity of the solution in this scale of Besov spaces is investigated with the aim of determining the largest for which the solution is in B(Lr()). The regularity theorems given in this paper build upon the recent results of Jerison and Kenig [10]. The proof of the regularity theorem uses characterizations of Besov spaces by wavelet expansions.

authors

• Devore, Ronald

published proceedings

• Communications in Partial Differential Equations

author list (cited authors)

• Dahlke, S., & Devore, R. A.

citation count

• 86

complete list of authors

• Dahlke, Stephan||Devore, Ronald A

publication date

• January 1997

publisher

• Taylor & Francis  Publisher

published in

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS  Journal

Digital Object Identifier (DOI)

• 10.1080/03605309708821252

start page

• 1

end page

• 16

volume

• 22

issue

• 1-2

URL

• http://dx.doi.org/10.1080/03605309708821252