# Tagged Questions

Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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### A priori estimate for diffraction problem for linear elliptic PDEs

I am looking for a reference to show how to obtain a priori estimate of the solution $u\in H^1$ and $u\in C^{2,\alpha}$ to the diffraction problem of linear elliptic equation. I looked at ...
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### Commutator representation of certain smoothing operators

I have a question regarding the classical trace $\text{Tr} \colon \Psi^{-\infty}(S^1)\to \mathbb C$ on pseudodifferential operators of infinite negative order (i.e. smoothing operators), defined over ...
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### Compact Eucledean hypersurfaces with “almost” constant H_k curvature

Let $M$ be an Eucledean $n$-dimensional compact hypersurface with constant $H_k$ curvature, where $k=1,...n$. A theorem by A.Ros tell us that so $M$ is an Eucledean sphere. Does anybody know if there ...
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### Reference for a Heat Process in a Wedge

I would like to ask about an explicit suggestion/reference for the following type of heat processes: Roughly, assume we have a "wedge" $W$ of the following form - a domain in $\mathbb{R}^n$ with a ...
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### Regularity result for Neumann problem

I have two questions. On Elliptic regularity for the Neumann problem, the OP asked whether the test function $v$ must be of mean value zero. However, isn't it true that we only need $f$ is of mean ...
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### method for global existance for the NLS

We consider the nonlinar Schr\"odinger equation(NLS): $$i\frac{\partial u}{\partial t}+\Delta_{x}u +\lambda |u|^{2k}u =0, \ u(x, 0)= u_{0}(x);$$ where $\lambda \in \mathbb R, \ k \in \mathbb N,$ ...
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### separable BV space for PDE's, Whats stopping us? [closed]

Consider the metric space BV(0,1) with the following metric $$d(u,v) = \|u-v\|_{L^1} + |TV(u)-TV(v)|$$. It is separable, compact, uniformly bounded and complete. So What is the really obvious thing ...
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