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.
Qun Lin, Hehu Xie, Fei Xu (2015)
Applications of Mathematics
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A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated...
Gabriella Tarantello, Stanley Alama (1996)
Mathematische Zeitschrift
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Nazarov, A.I. (2004)
Journal of Mathematical Sciences (New York)
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Devdariani, G. (2000)
Bulletin of TICMI
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K. I. Iordanidis (1971)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
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Alves, C.O., Concalves, J.V., Maia, L.A. (1996)
Abstract and Applied Analysis
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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.
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.
Joseph H. Silverman (2012)
Acta Arithmetica
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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.