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Results tagged with ap.analysis-of-pdes
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user 50621
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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When does $\{u\in H^1_0: \Delta_{\mu}u\in L^2\}=H_0^1\cap H^2$.
Let $(M,\mu)$ be a weighted Riemannian manifold. In Grigor’yan's book, he proves that the Dirichlet Laplacian $\Delta_{\mu}$ is self-adjoint on the set $u\in\{u\in H^1_0(M): \Delta_{\mu}u\in L^2\}$. I …
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