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Results tagged with ap.analysis-of-pdes
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user 90407
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
Accepted
$L^p$ regularity for semidisc
No, you need some information on what $\psi$ does on the real line. A counterexample for your estimate is given by the bounded harmonic function $$ \psi(x,y)=\arctan\frac xy, $$ which does not even be …
- 336
3
votes
Regularity of Laplace equation with Dirichlet data on a part of the boundary
No. Take $u(x,y)=\Re \sqrt{x+iy}$ then $u$ is harmonic in the slit plane, and satisfies homogeneous Dirichlet conditions in $\{x<0\}$ and homogeneous Neumann conditions on $\{x>0\}$. You can now const …
- 336