Gradient regularity for quasilinear elliptic Dirichlet problems in the plane

2016 ◽  
Vol 145 ◽  
pp. 143-161 ◽  
Author(s):  
Angela Alberico ◽  
Andrea Cianchi ◽  
Carlo Sbordone
Keyword(s):  
Dirichlet Problems ◽  
Quasilinear Elliptic ◽  
Gradient Regularity

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz–Sobolev spaces

2012 ◽  
Vol 75 (12) ◽  
pp. 4441-4456 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giovanni Molica Bisci ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Sobolev Spaces ◽  
Dirichlet Problems ◽  
Quasilinear Elliptic

Comparison results in second order quasilinear Dirichlet problems

1991 ◽  
Vol 118 (1-2) ◽  
pp. 91-103 ◽  
Author(s):  
L. E. Payne ◽  
J. R. L. Webb
Keyword(s):  
Elliptic Equations ◽  
Second Order ◽  
Quasilinear Elliptic Equations ◽  
Dirichlet Problems ◽  
Comparison Results ◽  
Special Cases ◽  
Quasilinear Elliptic ◽  
Comparison Technique

SynopsisIn [6] and [9] two different methods are given for comparing solutions of Dirichlet problems for second order quasilinear elliptic equations on convex regions. In this paper a general comparison technique is outlined—one which contains the methods of [6] and [9] as special cases. This technique is then applied to a number of special examples, comparisons with known results are given and a number of possible extensions are indicated.

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