scholarly journals Neumann problems for nonlinear elliptic equations with L1 data

2015 ◽  
Vol 259 (3) ◽  
pp. 898-924 ◽  
Author(s):  
M.F. Betta ◽  
O. Guibé ◽  
A. Mercaldo
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Neumann Problems ◽  
Nonlinear Elliptic ◽  
L1 Data

scholarly journals On a nonlinear elliptic problems having large monotonocity with L1-data in weighted Orlicz-Sobolev spaces

2019 ◽  
Vol 5 (1) ◽  
pp. 104-116
Author(s):  
Badr El Haji ◽  
Mostafa El Moumni ◽  
Khaled Kouhaila
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Entropy Solution ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Monotonicity Condition ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data

AbstractWe prove in weighted Orlicz-Sobolev spaces, the existence of entropy solution for a class of nonlinear elliptic equations of Leray-Lions type, with large monotonicity condition and right hand side f ∈ L1(Ω).

Nonlinear Elliptic Equations with L1 Data as Limit of Bilateral Problems

1997 ◽  
Vol 07 (02) ◽  
pp. 151-164 ◽  
Author(s):  
Luigi Orsina
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Entropy Solutions ◽  
Nonlinear Elliptic ◽  
L1 Data

In this paper we prove that entropy solutions for nonlinear elliptic equations with L1 data can be obtained as limit as n tends to infinity of the sequence {un} of solutions of the bilateral problems with obstacles n and -n associated to the same equations.

scholarly journals Uniqueness for Neumann problems for nonlinear elliptic equations

2019 ◽  
Vol 18 (3) ◽  
pp. 1023-1048
Author(s):  
Maria Francesca Betta ◽  
◽  
Olivier Guibé ◽  
Anna Mercaldo ◽  
◽  
...  
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Neumann Problems ◽  
Nonlinear Elliptic

scholarly journals Existence of entropy solutions for nonlinear elliptic equations in Musielak framework with L1 data

2018 ◽  
Vol 36 (1) ◽  
pp. 125 ◽  
Author(s):  
Elemine Vall Mohamed Saad Bouh ◽  
A. Ahmed ◽  
A. Touzani ◽  
A. Benkirane
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Equations ◽  
Entropy Solutions ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data ◽  
The Right

We prove existence of solutions for strongly nonlinear elliptic equations of the form $$ \left\{\begin{array}{c} A(u)+g(x,u,\nabla u)=f+\mbox {div}(\phi(u))\quad \textrm{in }\Omega, \\ u\equiv0\quad \partial \Omega. \end{array} \right.$$ Where $A(u)=-\mbox {div}(a(x,u,\nabla u))$ be a Leray-Lions operator defined in $D(A)\subset W^{1}_{0}L_\varphi(\Omega) \rightarrow W^{-1}_{0}L_\psi(\Omega)$, the right hand side belongs in $ L^{1}(\Omega)$, and $\phi\in C^{0}(\mathbb{R},\mathbb{R}^N)$, without assuming the $\Delta_{2}$-condition on the Musielak function.

scholarly journals On degenerate fully nonlinear elliptic equations in balls

1987 ◽  
Vol 35 (2) ◽  
pp. 299-307 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Elliptic Equations ◽  
Existence Theorems ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Neumann Problems ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Monge Ampere ◽  
Special Case ◽  
Nonlinear Degenerate

We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.

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