On $gamma$-weak solutions of elliptic equations
On $gamma$-weak solutions of elliptic equations
Summary: We build on the `alternative' approach to the Dirichlet problem in weighted Sobolev spaces to formulate sufficient conditions for interior regularity of \(\gamma\)-weak solutions of the Dirichlet problem for second order elliptic PDEs with Lipschitz coefficients. Next, we prove a maximum principle (for \(\gamma\)-weak subsolutions). Last, we generalize (from power type weights to a larger class of weights) a trace theorem by J. Necas.
- University of Basilicata Italy
Second-order elliptic equations, trace theorem, Smoothness and regularity of solutions to PDEs, interior regularity, \(\gamma\)-weak subsolutions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, weighted Sobolev spaces
Second-order elliptic equations, trace theorem, Smoothness and regularity of solutions to PDEs, interior regularity, \(\gamma\)-weak subsolutions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, weighted Sobolev spaces
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