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The connections between Dirichlet, regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mayboroda, Svitlana |
| Copyright Year | 2010 |
| Abstract | Abstract The present paper discusses relations between regularity, Dirichlet, and Neumann problems. We investigate the boundary problems for block operators and prove, in particular, that the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem for general elliptic operators with complex bounded measurable coefficients. This is strikingly different from the case of real operators, for which such an implication was established in 1993 by C. Kenig, J. Pipher [Invent. Math. 113 (3) (1993) 447–509] and since then has served as an integral part of many results. |
| Starting Page | 1786 |
| Ending Page | 1819 |
| Page Count | 34 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.aim.2010.04.019 |
| Volume Number | 225 |
| Alternate Webpage(s) | http://www-users.math.umn.edu/~svitlana/RD9.pdf |
| Alternate Webpage(s) | http://www.math.umn.edu/~svitlana/RD9.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.aim.2010.04.019 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
