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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.

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Sobolev norms of eigenfunctions

Let me make the question more precise -- f is normalized to have L^2 norm 1. Then f is in $H^1_0(D)$ and the Sobolev 1-norm of f is \lambda. We want the norm of f in H^s(D). I'll be glad if anybody …
Debraj Chakrabarti's user avatar