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Results tagged with ap.analysis-of-pdes
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user 6360
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
Laplace equation with mixed boundary conditions
The solution to the Dirichlet problem is unique by the maximum principle. For the same reason, the solution to the Neumann problem is unique up to a constant.
At worst your problem would fail uniquen …
- 817
1
vote
0
answers
367
views
Definition of spectral gradient
Consider this differential operator
$$
\mathcal{H}(\phi(\mathbf{x})) = -\triangle + V(\mathbf{x})H_\epsilon (\phi(\mathbf{x}))
$$
where $\mathbf{x} \in \mathbb{R}^2$, $\phi : \mathbb{R}^2 \rightarrow …
- 817