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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.
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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 …
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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 …