Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains

2012 ◽  
Vol 49 (1-2) ◽  
pp. 37-76 ◽  
Author(s):  
Sun-Sig Byun ◽  
Dian K. Palagachev
Keyword(s):  
Elliptic Equations ◽  
Regularity Of Solutions ◽  
Quasilinear Elliptic Equations ◽  
Reifenberg Flat Domains ◽  
Morrey Regularity ◽  
Reifenberg Flat ◽  
Quasilinear Elliptic

scholarly journals Global W1,p(·) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains

2018 ◽  
Vol 7 (4) ◽  
pp. 517-533 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Elliptic Equations ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Lebesgue Spaces ◽  
Quasilinear Equations ◽  
Bmo Coefficients ◽  
Reifenberg Flat ◽  
Quasilinear Elliptic

AbstractIn this paper, we prove the gradient estimate for renormalized solutions to quasilinear elliptic equations with measure data on variable exponent Lebesgue spaces with BMO coefficients in a Reifenberg flat domain.

scholarly journals Solvability of quasilinear elliptic equations with strong dependence on the gradient

2000 ◽  
Vol 5 (3) ◽  
pp. 159-173 ◽  
Author(s):  
Darko Žubrinić
Keyword(s):  
Elliptic Equations ◽  
Strong Dependence ◽  
Strong Solutions ◽  
Outer Radius ◽  
Regularity Of Solutions ◽  
Quasilinear Elliptic Equations ◽  
A Posteriori ◽  
The Right ◽  
Equation Solvability ◽  
Quasilinear Elliptic

We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involvingp-Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro-differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem. We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.

A note on the boundary regularity of solutions to quasilinear elliptic equations

2018 ◽  
Vol 24 (2) ◽  
pp. 849-858 ◽  
Author(s):  
Giuseppe Riey ◽  
Berardino Sciunzi
Keyword(s):  
Laplace Operator ◽  
Critical Points ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Boundary Regularity ◽  
Regularity Of Solutions ◽  
Quasilinear Elliptic Equations ◽  
Second Derivatives ◽  
Quasilinear Elliptic ◽  
Derivatives Of

We study the summability up to the boundary of the second derivatives of solutions to a class of Dirichlet boundary value problems involving the p-Laplace operator. Our results are meaningful for the cases when the Hopf’s Lemma cannot be applied to ensure that there are no critical points of the solution on the boundary of the domain.

Sign in / Sign up

Export Citation Format

Share Document