6533b872fe1ef96bd12d3807
RESEARCH PRODUCT
OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS
Fuensanta AndreuJulián ToledoJosé M. MazónNoureddine Igbidasubject
Pure mathematicsElliptic operatorMonotone polygonApplied MathematicsModeling and SimulationWeak solutionBounded functionObstacle problemMathematical analysisBoundary value problemUniquenessType (model theory)Mathematicsdescription
In this paper we study the questions of existence and uniqueness of solutions for equations of type - div a(x,Du) + γ(u) ∋ ϕ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x,Du) · η + β(u) ∋ ψ. The nonlinear elliptic operator div a(x,Du) modeled on the p-Laplacian operator Δp(u) = div (|Du|p-2Du), with p > 1, γ and β maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) ∩ β(0), [Formula: see text] and the data ϕ ∈ L1(Ω) and ψ ∈ L1(∂ Ω). Since D(γ) ≠ ℝ, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solution has to be introduced.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-11-01 | Mathematical Models and Methods in Applied Sciences |