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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

2 votes
0 answers
44 views

Potential scattering for non-decaying potential

I am reading this note on potential scattering by Siu-Hung Tang and Maciej Zworski. Just wondering if there is a scattering theory for the Schrödinger with a non-decaying potential $- \Delta + V$ on t …
3 votes
1 answer
370 views

Poincare constant on non-convex domain

I'm wondering if there is any results on the optimal constant for the Poincare inequality on a non-convex domain in $\mathbb{R}^3$, since most of the things I found are results on convex ones. Any r …
1 vote
1 answer
171 views

Lower bound of the spectrum of a Schrodinger operator on a bounded domain

I am trying to look for references on estimate of the lower bound of the spectrum of a Schrodinger operator $-\Delta + V$ on a bounded domain in three-dimensional space. For simplicity, we can take th …