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 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.

Qualitative Analysis of Solutions for a Class of Anisotropic Elliptic Equations with Variable Exponent

2015 ◽  
Vol 59 (3) ◽  
pp. 541-557 ◽  
Author(s):  
G. A. Afrouzi ◽  
M. Mirzapour ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Weak Solution ◽  
Variational Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Special Form ◽  
Variable Exponent ◽  
Nonlinear Term ◽  
Fountain Theorem ◽  
Image Position ◽  
Anisotropic Elliptic Equations

AbstractWe are concerned with the degenerate anisotropic problemWe first establish the existence of an unbounded sequence of weak solutions. We also obtain the existence of a non-trivial weak solution if the nonlinear termfhas a special form. The proofs rely on the fountain theorem and Ekeland's variational principle.

scholarly journals Continuous solutions to two iterative functional equations

2021 ◽  
Author(s):  
Karol Baron
Keyword(s):  
Probability Measure ◽  
Functional Equations ◽  
Continuous Functions ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$ φ of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$ φ ( x ) = F ( x ) - ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , φ ( x ) = F ( x ) + ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , where P is a probability measure on a $$\sigma $$ σ -algebra of subsets of $$\Omega $$ Ω .

scholarly journals Yang–Mills Measure on the Two-Dimensional Torus as a Random Distribution

2019 ◽  
Vol 372 (3) ◽  
pp. 1027-1058
Author(s):  
Ilya Chevyrev
Keyword(s):  
Random Distribution ◽  
Random Variable ◽  
Continuous Functions ◽  
Small Scale ◽  
Dimensional Torus ◽  
Hölder Continuous ◽  
Line Segments ◽  
Yang Mills ◽  
Hölder Continuous Functions ◽  
On Line

Abstract We introduce a space of distributional 1-forms $$\Omega ^1_\alpha $$Ωα1 on the torus $$\mathbf {T}^2$$T2 for which holonomies along axis paths are well-defined and induce Hölder continuous functions on line segments. We show that there exists an $$\Omega ^1_\alpha $$Ωα1-valued random variable A for which Wilson loop observables of axis paths coincide in law with the corresponding observables under the Yang–Mills measure in the sense of Lévy (Mem Am Math Soc 166(790), 2003). It holds furthermore that $$\Omega ^1_\alpha $$Ωα1 embeds into the Hölder–Besov space $$\mathcal {C}^{\alpha -1}$$Cα-1 for all $$\alpha \in (0,1)$$α∈(0,1), so that A has the correct small scale regularity expected from perturbation theory. Our method is based on a Landau-type gauge applied to lattice approximations.

Radiative effects for some bidimensional thermoelectric problems

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Luisa Consiglieri
Keyword(s):  
Steady State ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Divergence Form ◽  
Radiative Effects ◽  
Existence Of Weak Solutions ◽  
Nonlinear Radiation ◽  
Radiation Type

AbstractThere are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a

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