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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.

2 votes
1 answer
372 views

Asymptotic behaviour near the boundary in the Dirichlet problem for the Laplacian.

Perturbative behaviour of solutions of the solutions of the Dirichlet problem for the Laplacian: Lets consider $ B = B(0, 1) \in \mathbb{R}^2$ be the unit circle with center at $0\in\mathbb{R}^2$. Le …
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