Abstract
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 language | English |
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Title of host publication | Operator Theory |
Subtitle of host publication | Advances and Applications |
Pages | 99-134 |
Number of pages | 36 |
DOIs | |
State | Published - 2018 |
Publication series
Name | Operator Theory: Advances and Applications |
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Volume | 269 |
ISSN (Print) | 0255-0156 |
ISSN (Electronic) | 2296-4878 |
Bibliographical note
Publisher Copyright:© Springer Nature Switzerland AG 2018.
ASJC Scopus subject areas
- Analysis