APPLICATIONS OF THE THREE CRITICAL POINTS THEOREM IN QUASILINEAR ELLIPTIC EQUATIONS

1985 ◽  
Vol 5 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Yaotian Shen ◽  
Xinkang Guo
Keyword(s):  
Critical Points ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Three Critical Points Theorem ◽  
Quasilinear Elliptic

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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