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Regularity of solution to Laplacian equation with Neumann data on Lipschitz domain

Let $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$ and let $u\in H^1(\Omega)$ be a weak solution to \begin{equation} \begin{cases} -\Delta u=0 \quad &\mbox{in $\Omega$}\\ \frac{\partial ...
student's user avatar
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2 votes
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Clarification about solvability of Dirichlet problem at infinity on a pinched negative curvature space

Let $M$ be a complete Riemannian manifold of pinched negative curvature $(-a^2 \leq K \leq -b^2 < 0)$. Let $M_\infty$ denote the ideal boundary and $\varphi \in C^0(M_\infty)$ be a prescribed "...
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1 vote
0 answers
65 views

Equivalence of $L^p$ harmonic functions on the ball and a representation by harmonic homogeneous polynomials

In Harmonic function theory, there is a theorem which says that if $u$ is an harmonic function on $B\left(a,r\right)$, then there exist homogeneous harmonic polynomials $p_{m}$ in $\mathbb{R}^{n}$ ...
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1 vote
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Wavelets in the spaces of harmonic functions

I plan to do something with the theory of wavelets but in harmonic function theory. My question is about this interconnection between wavelets and harmonic functions. Can you recommend me some paper ...
Alem's user avatar
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Function Spaces on the Open Unit Disk defined by Hardy Space norms

I've been reading up on Hardy spaces and (sub)harmonic functions over the open unit disk $\mathbb{D}\subset\mathbb{C}$, and I've found myself working with atypical objects in mostly-typical situations....
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