scholarly journals Renormalized solutions of Dirichlet problems for quasilinear elliptic equations with general measure data

2008 ◽  
Vol 38 (1) ◽  
pp. 51-93 ◽  
Author(s):  
F. Maeda
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Dirichlet Problems ◽  
Renormalized Solutions ◽  
General Measure ◽  
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.

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.

scholarly journals Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

2020 ◽  
Vol 44 (4) ◽  
pp. 617-637
Author(s):  
T. AHMEDATT ◽  
A. AHMED ◽  
H. HJIAJ ◽  
A. TOUZANI
Keyword(s):  
Dirichlet Problem ◽  
Growth Condition ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Renormalized Solutions ◽  
Carathéodory Function ◽  
Regularity Results ◽  
Quasilinear Elliptic

In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.

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