On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
Mohamed El Ouaarabi, Chakir Allalou, Saïd Melliani
Abstract
Abstract We prove the existence and uniqueness of a weak solution to a Dirichlet boundary value problem for a class of nonlinear degenerate elliptic equations in the setting of weighted Sobolev spaces. Our proof is based on the weighted Sobolev spaces theory and the Browder–Minty theorem. First, we transform the problem into an equivalent operator equation; second, we utilized the Browder–Minty theorem to prove the existence and uniqueness of a weak solution to the considered problem.
Topics & Concepts
MathematicsSobolev spaceUniquenessDegenerate energy levelsPure mathematicsClass (philosophy)Mathematical analysisNonlinear systemSobolev inequalityDirichlet problemSobolev spaces for planar domainsBoundary value problemElliptic boundary value problemDirichlet distributionInterpolation spaceFunctional analysisFree boundary problemGeneArtificial intelligencePhysicsChemistryBiochemistryQuantum mechanicsComputer scienceNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems