Regularity for the dirichlet problem

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter is devoted to the study of uniform boundary regularity estimates for the Dirichlet problem [Formula presented.] where Lε =div(A(x/ε)∇). Assuming that the coefficient matrix A = A(y) is elliptic, periodic, and belongs to VMO(ℝd), we establish uniform boundary Hölder and W1, p estimates in C1 domains Ω. We also prove uniform boundary Lipschitz estimates in C1, α domains under the assumption that A is elliptic, periodic, and Hölder continuous. As in the previous chapter for interior estimates, boundary Hölder and Lipschitz estimates are proved by a compactness method. The boundaryW1, p estimates are obtained by combining the boundary Hölder estimates with the interior W1, p estimates, via the real-variable method introduced in Section 4.2.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
Number of pages36
StatePublished - 2018

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2018.

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'Regularity for the dirichlet problem'. Together they form a unique fingerprint.

Cite this