# Tagged Questions

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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http://terrytao.wordpress.com/2008/07/07/hassells-proof-of-scarring-for-the-bunimovich-stadium/ I cannot relate how the eigenfunctions normalizaed correspond to the probabality distribution of the ...
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### Higher dimensional analogue of Kellog's theorem? (Holder continuity of solution to Dirichlet problem with Holder continuous boundary data)

Let $f:S^n\to C$ be a continuous function, $n\geq 1$. When $n=1$, this is a well-known theorem, called Kellog's theorem (or sometimes Kellog-Warschawski's theorem) which states the following Theorem: ...
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### Interior regularity for elliptic equations

The monograph "Non-Homogeneous Boundary Value Problems and Applications" by Lions and Magenes is infamous for developing a truly extensive regularity theory for elliptic problems on domains, and for ...
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### why is it called the diamagnetic inequality?

How is the Diamagnetic inequality born? Why is it call this name? Diamagnetic inequality： $\big|\nabla|u|(x)\big|\leq \big|(\nabla+iA)u(x)\big|$.
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### Nash's paper on parabolic equations.

I am currently studying the paper "CONTINUITY OF SOLUTIONS OF PARABOLIC AND ELLIPTIC EQUATIONS" by John Nash (cf. American Journal of Mathematics, Vol. 80, 1958). The author there establishes some a ...
I've been given the following BVP: \begin{align*} -\Delta u = u- u^3,\: x\in \Omega \end{align*}\begin{align} u = 0,\: x\in \partial \Omega \end{align} where $\Omega\subset \mathbb{R}^N$ is bounded. ...