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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 20
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 4, August 2013
  4. Large viscosity solutions for some fully nonlinear equations
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 6, December 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 4, August 2013
The Aubry set for a version of the Vlasov equation
Large viscosity solutions for some fully nonlinear equations
Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion
On mountain pass type algorithms
Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations
Positive solution to semilinear parabolic equation associated with critical Sobolev exponent
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 3, June 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 2, April 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 1, February 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Large viscosity solutions for some fully nonlinear equations

Content Provider SpringerLink
Author Alarcón, S. Quaas, A.
Copyright Year 2013
Abstract We study existence, uniqueness and asymptotic behavior near the boundary of solutions of the problem $$\left\{\begin{array}{ll}-F(D^{2} u) + \beta (u) = f \quad {\rm in} \, \Omega, \\ u = + \infty \quad \quad \quad \quad \quad \quad \,\,\,\, {\rm on}\, \partial \Omega, \end{array} \right.\quad \quad \quad \quad \quad {\rm (P)}$$ where Ω is a bounded smooth domain in $${{\mathbb R}^N, N >1 , F}$$ is a fully nonlinear elliptic operator and β is a nondecreasing continuous function. Assuming that β satisfies the Keller–Osserman condition, we obtain existence results which apply to $${f \in L^\infty_{loc}(\Omega)}$$ or f having only local integrability properties where viscosity solutions are well defined, i.e. $${f \in L^N_{loc}(\Omega)}$$ . Besides, we find the asymptotic behavior near the boundary of solutions of (P) for a wide class of functions $${f \in \mathcal{C}(\Omega)}$$ . Based in this behavior, we also prove uniqueness.
Ending Page 1472
Page Count 20
Starting Page 1453
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 20
Language English
Publisher Springer Basel
Publisher Date 2013-02-08
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Fully nonlinear operator Keller–Osserman condition Analysis Asymptotic behavior Uniqueness Boundary blow-up Boundary values of solutions to elliptic equations Nonlinear elliptic equations Asymptotic behavior of solutions Blow-up Viscosity solutions
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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