On the Eikonal equation for degenerate elliptic operators [PDF]
Proceedings of the American Mathematical Society, 2011 We consider the nonnegative viscosity solution of the homogeneous Dirichlet problem for an eikonal equation associated to an operator sum of squares of vector fields of Grushin type in a symmetric domain. We show that the solution is locally Lipschitz continuous except at the characteristic boundary point.
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Generalized Keller-Osserman Conditions for Fully Nonlinear Degenerate Elliptic Equations
Современная математика: Фундаментальные направления, 2018 We discuss the existence of entire (i.e. defined on the whole space) subsolutions of fully nonlinear degenerate elliptic equations, giving necessary and sufficient conditions on the coefficients of the lower order terms which extend the classical Keller ...
I Capuzzo Dolcetta, F Leoni, A Vitolo
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Maximum principles for viscosity solutions of weakly elliptic equations
Bruno Pini Mathematical Analysis Seminar, 2019 Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions.
Antonio Vitolo
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Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient
Boundary Value Problems, 2007 We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and Liouville-type theorems to obtain a ...
Sebastian Lorca, Leonelo Iturriaga
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Application of the Stampacchia lemma to anisotropic degenerate elliptic equations
Journal of Innovative Applied Mathematics and Computational Sciences, 2023 In this paper, we prove the existence and regularity of solutions for a class of nonlinear anisotropic degenerate elliptic equations with the data f belonging to certain Marcinkiewicz spaces Mm(Ω) with m > 1.
Hichem
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Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2015 Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built.
R.M. Askhatov, R.N. Abaydullin
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Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations
Moroccan Journal of Pure and Applied Analysis, 2019 In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic ...
Cavalheiro Albo Carlos
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Weighted W1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains
Advances in Nonlinear Analysis, 2021 Let w be a Muckenhoupt A2(ℝn) weight and Ω a bounded Reifenberg flat domain in ℝn. Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition.
Zhang Junqiang, Yang Dachun, Yang Sibei
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On a class of degenerate elliptic equations [PDF]
Nagoya Mathematical Journal, 1974 We shall prove in Chapter I the hypoellipticity for a class of degenerate elliptic operators of higher order. Chapter II will be devoted to the consideration of the regularity at the boundary for the solutions of general boundary problems for the equations considered in Chapter I being restricted to the second order.
Hashimoto, Yoshiaki, Matsuzawa, Tadato
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Gradient bounds for solutions of nonlinear strictly elliptic equations, applications and extensions
ITM Web of Conferences, 2018 In this short manuscript, we briefly recall some well-known methods for obtaining gradient bounds of viscosity solutions for elliptic and parabolic equations.
Duc Nguyen Vinh
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