On a linear second order degenerate elliptic equation.
Devdariani, G. (2000)
Bulletin of TICMI
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Devdariani, G. (2000)
Bulletin of TICMI
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Nazarov, A.I. (2004)
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K. I. Iordanidis (1971)
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Nestke, A., Zickermann, F.
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Joseph H. Silverman (2012)
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Jani Onninen, Xiao Zhong (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.
Giovanni Anello (2005)
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.
Joseph H. Silverman, Katherine E. Stange (2011)
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Flavia Giannetti
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Tiantian Qiao, Weiguo Li, Kai Liu, Boying Wu (2014)
Annales Polonici Mathematici
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The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.