Albo Carlos Cavalheiro (2018)
Commentationes Mathematicae Universitatis Carolinae
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The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.
Rüdiger Landes (1989)
Manuscripta mathematica
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H. Marcinkowska (1963)
Studia Mathematica
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Alves, C.O., Concalves, J.V., Maia, L.A. (1996)
Abstract and Applied Analysis
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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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Michael Meier (1981)
Mathematische Zeitschrift
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K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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Cyril Imbert, Luis Silvestre (2016)
Journal of the European Mathematical Society
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We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.
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.
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.