scholarly journals Regularity of solutions for a class of quasilinear elliptic equations related to the Caffarelli-Kohn-Nirenberg inequality

2021 ◽  
pp. 125474
Author(s):  
Le Cong Nhan ◽  
Ky Ho ◽  
Le Xuan Truong
Keyword(s):  
Elliptic Equations ◽  
Regularity Of Solutions ◽  
Quasilinear Elliptic Equations ◽  
Nirenberg Inequality ◽  
Quasilinear Elliptic

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.

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