Optimal Regularity of a Degenerate Elliptic Equation
Journal of Nonlinear Mathematical Physics, 2022 AbstractIn this paper, we consider the optimal regularity of solutions to elliptic equation with a Grushin-like operator. By using the Feynman–Kac formula, we first get the expression of heat kernel, and then by using the properties of heat kernel, the optimal regularity of solutions will be obtained.
Xiaohuan Wang, Jihui Zhang
openaire +2 more sources
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
doaj +2 more sources
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
doaj
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
doaj +1 more source
Local Gradient Estimates for Degenerate Elliptic Equations [PDF]
Advanced Nonlinear Studies, 2016 Abstract This paper is focused on the local interior W 1 , ∞
Hoang, Luan, Nguyen, Truyen, Phan, Tuoc
openaire +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
An oscillation theorem for the nonlinear degenerate elliptic equation in the Heisenberg group
Boundary Value Problems, 2021 The aim of this paper is to study the oscillation of solutions of the nonlinear degenerate elliptic equation in the Heisenberg group H n $H^{n}$ . We first derive a critical inequality in H n $H^{n}$ . Based on it, we establish a Picone-type differential
Duan Wu, Pengcheng Niu
doaj +1 more source
Comparison of critical behaviors of elliptic and hyperbolic quadratic algebraic equations with variable coefficients [PDF]
INCAS Bulletin, 2015 A comparison of the behaviours of the elliptic with those of hyperbolic quadratic algebraic equations (QAEs) with free and linear variable coefficients, in vicinity of their critical surfaces is made.
Adriana NASTASE
doaj +1 more source