scholarly journals Nonunique continuation for uniformly parabolic and elliptic equations in selfadjoint divergence form with Hölder continuous coefficients

1973 ◽  
Vol 79 (2) ◽  
pp. 350-355 ◽  
Author(s):  
Keith Miller
Keyword(s):  
Elliptic Equations ◽  
Divergence Form ◽  
Hölder Continuous

scholarly journals Generalizing Hopf’s Boundary Point Lemma

2019 ◽  
Vol 62 (1) ◽  
pp. 183-197 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Weak Solutions ◽  
Lower Order ◽  
Boundary Point ◽  
Elliptic Equations ◽  
Morrey Space ◽  
Divergence Form ◽  
Hölder Continuous

AbstractWe give a Hopf boundary point lemma for weak solutions of linear divergence form uniformly elliptic equations, with Hölder continuous top-order coefficients and lower-order coefficients in a Morrey space.

Local Hölder estimates for non-uniformly variable exponent elliptic equations in divergence form

2017 ◽  
Vol 148 (1) ◽  
pp. 211-224 ◽  
Author(s):  
Fengping Yao
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Continuous Functions ◽  
Divergence Form ◽  
Hölder Continuous ◽  
Special Model ◽  
Hölder Continuous Functions ◽  
Image Position ◽  
Hölder Estimates

In this paper we obtain the local Hölder regularity of the gradients of weak solutions for a class of non-uniformly nonlinear variable exponent elliptic equations in divergence formincluding the following special modelunder some proper assumptions on Ai and the Hölder continuous functions f, pi(x) for i = 1, 2.

scholarly journals Weighted W 1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains

2021 ◽  
Vol 11 (1) ◽  
pp. 535-579
Author(s):  
Junqiang Zhang ◽  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Divergence Form ◽  
Degenerate Elliptic Equations ◽  
Hölder Continuous ◽  
Weighted Bmo ◽  
Degenerate Elliptic ◽  
Order Degenerate ◽  
Bmo Spaces ◽  
Reifenberg Flat

Abstract Let w be a Muckenhoupt A 2(ℝ n ) weight and Ω a bounded Reifenberg flat domain in ℝ n . Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition. In this article, the authors investigate the weighted W 1, p (·)(Ω, w)-regularity of the weak solutions of second order degenerate elliptic equations in divergence form with Dirichlet boundary condition, under the assumption that the degenerate coefficients belong to weighted BMO spaces with small norms.

MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS

2007 ◽  
Vol 18 (09) ◽  
pp. 1071-1111 ◽  
Author(s):  
JÉRÔME VÉTOIS
Keyword(s):  
Continuous Function ◽  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Nonlinear Elliptic Equations ◽  
Beltrami Operator ◽  
Hölder Continuous ◽  
Nonlinear Elliptic

Let (M,g) be a smooth compact Riemannian n-manifold, n ≥ 4, and h be a Holdër continuous function on M. We prove multiplicity of changing sign solutions for equations like Δg u + hu = |u|2* - 2 u, where Δg is the Laplace–Beltrami operator and 2* = 2n/(n - 2) is critical from the Sobolev viewpoint.

scholarly journals Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations

2020 ◽  
Author(s):  
Ariel Barton ◽  
Steve Hofmann ◽  
Svitlana Mayboroda
Keyword(s):  
Neumann Problem ◽  
Elliptic Equations ◽  
Divergence Form ◽  
Higher Order ◽  
Elliptic Operators ◽  
Layer Potentials ◽  
The Neumann Problem

Abstract We solve the Neumann problem, with nontangential estimates, for higher-order divergence form elliptic operators with variable $t$-independent coefficients. Our results are accompanied by nontangential estimates on higher-order layer potentials.

Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains

2014 ◽  
Vol 66 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Jorge Rivera-Noriega
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Carleson Measure ◽  
Divergence Form ◽  
Second Order ◽  
Linear Operators ◽  
Dirichlet Problems ◽  
Small Perturbations ◽  
Cylindrical Domains

AbstractFor parabolic linear operators L of second order in divergence form, we prove that the solvability of initial Lp Dirichlet problems for the whole range 1 < p < ∞ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of L satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of p > 1, the initial Lp Dirichlet problem associated with Lu = 0 over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.

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