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Results tagged with elliptic-pde
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user 8799
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
4
votes
1
answer
412
views
Simplicity of eigenvalues of an elliptic operator under a symmetry assumption
A striking difference in the spectral analysis of 2nd order elliptic boundary-value problems between one and several space dimensions is the following. In one space dimension, the eigenvalues are simp …
- 52.3k
9
votes
1
answer
205
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Geometry of the positive definite cone, versus homogenization of elliptic PDEs
Homogenization is a process that assigns to a positive definite-valued map $x\mapsto S(x)$ a non-trivial but physically meaningful average $\bar S$. There are various settings, for instance stochastic …
- 52.3k
5
votes
1
answer
163
views
Reinforced Maximum Principle
Let $U\subset{\mathbb R}^n$ be a bounded open domain with smooth boundary. I assume that $U$ is diffeomorphic to a ball. You may think of $L=\Delta$ and $U$ is the unit ball.
Let $L=\operatorname{div} …
- 52.3k
7
votes
1
answer
385
views
Convex solutions of the Poisson equation
Let $D$ be a planar, bounded, convex open domain. Given a positive function $f:D\to(0,+\infty)$, let us consider the Poisson equation
$$\Delta u=f\quad\hbox{in }D.$$
Not specifying any boundary condit …
- 52.3k