On the equivalence of stochastic completeness, Liouville and Khas'minskii condition in linear and nonlinear setting [PDF]
, 2012 Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss
Mari, Luciano, Valtorta, Daniele
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Free boundary problems for Tumor Growth: a Viscosity solutions approach [PDF]
, 2015 The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are generalized Hele-Shaw
Alt +14 more
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Equivalence of Viscosity and Weak Solutions for the $p(x)$-Laplacian [PDF]
, 2010 We consider different notions of solutions to the $p(x)$-Laplace equation $-\div(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with ...
Acerbi +29 more
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Sobolev gradients of viscosity supersolutions
Nonlinear Differential Equations and Applications NoDEA, 2023 We investigate which elliptic PDEs that have the property that every viscosity supersolution is $W^{1,q}_{loc}(Ω)$, $Ω\subseteq\mathbb{R}^n$. The asymptotic cone of the operator's sublevel set seems to be essential. It turns out that much can be said if we know how this cone compares to the sublevel set of a certain minimal operator associated with the
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The Parabolic Infinite-Laplace Equation in Carnot groups [PDF]
, 2014 By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups.
Bieske, Thomas, Martin, Erin
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Existence and asymptotic behavior of ground state solutions of semilinear elliptic system
Advances in Nonlinear Analysis, 2017 In this article, we take up the existence and the asymptotic behavior of entire bounded positive solutions to the following semilinear elliptic system:
Mâagli Habib +2 more
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Regularity of Supersolutions [PDF]
, 2012 The regularity for the supersolutions of the Evolutionary p-Laplace Equation is considered. In particular,the equivalence of viscosity supersolutions and p-supercaloric functions (lower semicontinuous supersolutions defined via a comparison principle) is considered.
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Multiple solutions for a system involving an anisotropic variable exponent operator
Boundary Value Problems, 2022 In this paper, the existence of a solution for an anisotropic variable exponent system is obtained and proved under general hypotheses. By considering additional conditions, it is proved a multiplicity result.
Leandro S. Tavares
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A rigorous setting for the reinitialization of first order level set equations [PDF]
, 2015 In this paper we set up a rigorous justification for the reinitialization algorithm. Using the theory of viscosity solutions, we propose a well-posed Hamilton-Jacobi equation with a parameter, which is derived from homogenization for a Hamiltonian ...
Hamamuki, Nao, Ntovoris, Eleftherios
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Combined effects in nonlinear singular elliptic problems in a bounded domain
Advances in Nonlinear Analysis, 2012 We establish an existence result of positive solutions to the following boundary value problem:
Chemmam Rym +3 more
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