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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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regularity of solutions of fractional laplacian
Hi, I think this paper is going to be useful for you
http://arxiv.org/abs/1004.1906
Do you have any information about Sobolev regularity for the function v solution of the extensio?n