Extension theory for Sobolev spaces on open sets with Lipschitz boundaries
Burenkov, Viktor I.
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Burenkov, Viktor I.
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Maria Alessandra Ragusa (1999)
Commentationes Mathematicae Universitatis Carolinae
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In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class for all and, as a consequence, the Hölder regularity of the solution . is an elliptic second order operator with discontinuous coefficients and the lower order terms belong to suitable Lebesgue spaces.
Chérif Amrouche, Hamid Bouzit (2008)
Applications of Mathematics
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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in theory.