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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.

3 votes
1 answer
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regularity of solution of linear elliptic PDE

I am interested in the boundary regularity of solutions of $ L(u) = f(x) \ge 0$ in $ \Omega$ with zero Dirichlet boundary conditions, here $L(u) = (-\Delta)^\frac{\alpha}{2}$ where $ 0 < \alpha <2$. …