The Robbins problem for elliptic equations in space
K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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Devdariani, G. (2000)
Bulletin of TICMI
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Nazarov, A.I. (2004)
Journal of Mathematical Sciences (New York)
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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 (2012)
Acta Arithmetica
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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.
B. Szafirski (1967)
Colloquium Mathematicae
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Joseph H. Silverman, Katherine E. Stange (2011)
Acta Arithmetica
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Nestke, A., Zickermann, F.
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Alves, C.O., Goncalves, J.V., Maia, L.A. (1998)
Abstract and Applied Analysis
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Albo Carlos Cavalheiro (2017)
Communications in Mathematics
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The main result establishes that a weak solution of degenerate semilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate semilinear elliptic equations.