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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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Dirichlet Problem Solvable when every component of the complement of the domain consists of ...

I read this sufficient condition for solvable boundary problem (Gilbarg & Trudinger 1998): "the boundary value problem is solvable if every component of the complement of the domain consists of more …
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