6533b7dafe1ef96bd126f422
RESEARCH PRODUCT
\( L^{1} \) existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions
Julián ToledoFuensanta AndreuJosé M. MazónNoureddine Igbidasubject
Pure mathematicsApplied MathematicsMathematical analysisSemi-elliptic operatorElliptic operatorHalf-period ratiop-LaplacianFree boundary problemBoundary value problemUniquenessLaplace operatorMathematical PhysicsAnalysisMathematicsdescription
Abstract In this paper we study the questions of existence and uniqueness of weak and entropy solutions for equations of type − div a ( x , D u ) + γ ( u ) ∋ ϕ , posed in an open bounded subset Ω of R N , with nonlinear boundary conditions of the form a ( x , D u ) ⋅ η + β ( u ) ∋ ψ . The nonlinear elliptic operator div a ( x , D u ) is modeled on the p-Laplacian operator Δ p ( u ) = div ( | D u | p − 2 D u ) , with p > 1 , γ and β are maximal monotone graphs in R 2 such that 0 ∈ γ ( 0 ) and 0 ∈ β ( 0 ) , and the data ϕ ∈ L 1 ( Ω ) and ψ ∈ L 1 ( ∂ Ω ) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-02-01 | Annales de l'Institut Henri Poincaré C, Analyse non linéaire |