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Results tagged with ap.analysis-of-pdes
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user 471159
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
Accepted
Exponential decay of resolvent kernel
The local statement is correct for any positive self-adjoint extension of the Laplace operator on a Riemannian manifold (not necessarily complete). It is an old result by Hoermander. See the proof of …
5
votes
Fredholm theory of non elliptic operators
I think I am in a good position to answer this. The Fredholm property of elliptic operators as maps between Sobolev spaces on compact manifolds rests on elliptic regularity properties. If an operators …