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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

1 vote
0 answers
48 views

How does the constant appearing in a priori estimate for the elliptic Dirichlet problem depe...

Someone, could you please tell me suitable references on how the constant $C$ appearing in the a priori estimate for the elliptic Dirichlet problem depends on the domain $\Omega$ ? More precisely, we …
kichr's user avatar
  • 11
0 votes
0 answers
180 views

Extending harmonic functions defined in the closure of a bounded smooth domain to some large...

Let $\Omega$ be a smooth bounded domain of $\mathbb{R}^N$ where $N\geq 2$. Consider the Laplace equation with a Neumann boundary condition $$ -\Delta u = 0 \quad\mbox{in } \Omega, \qquad \frac{\parti …
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  • 11