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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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Embeddings of Sobolev spaces on the unit disk
Is the space $W^{2,p}(\mathbf{U})$, compactly embedded to $W^{1,\infty}(\mathbf{U})$, where $\mathbf{U}$ is the unit disk.