Fully nonlinear second order elliptic equations : recent development
Nicolai V. Krylov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “On fully nonlinear elliptic equations of second order”
Fully nonlinear second order elliptic equations : recent development
New a priori estimates for -nonlinear elliptic systems with strong nonlinearities in the gradient, .
Arkhipova, A.A. (2004)
Journal of Mathematical Sciences (New York)
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Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations
N. Kutev (1991)
Archivum Mathematicum
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Estimates on elliptic equations that hold only where the gradient is large
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.
On existence of a unique generalized solution to systems of elliptic PDEs at resonance
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.
On a linear second order degenerate elliptic equation.
Devdariani, G. (2000)
Bulletin of TICMI
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The degenerate Venttsel' problem for elliptic equations.
Nazarov, A.I. (2004)
Journal of Mathematical Sciences (New York)
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Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations
Edward N. Dancer, Shusen Yan (2007)
Bollettino dell'Unione Matematica Italiana
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We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.
Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations.
Neil S. Trudinger (1988)
Revista Matemática Iberoamericana
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We prove comparison principles for viscosity solutions of nonlinear second order, uniformly elliptic equations, which extend previous results of P. L. Lions, R. Jensen and H. Ishii. Some basic pointwise estimates for classical solutions are also extended to continuous viscosity solutions.
Nonzero and positive solutions of a superlinear elliptic system
Mario Zuluaga Uribe (2001)
Archivum Mathematicum
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In this paper we consider the existence of nonzero solutions of an undecoupling elliptic system with zero Dirichlet condition. We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions and we give applications to biharmonic equations and the scalar case.
On some elliptic boundary-value problems with discontinuous nonlinearities
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.