Numerical integration in the discontinuous Galerkin method for elliptic problems
Prachař, Aleš, Najzar, Karel
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Prachař, Aleš, Najzar, Karel
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International Journal of Applied Mathematics and Computer Science
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Annales Polonici Mathematici
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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.
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Computational Methods in Applied Mathematics
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Annales Polonici Mathematici
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Applicationes Mathematicae
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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.