Survey on gradient estimates for nonlinear elliptic equations in various function spaces
Sookeun Byun, Dian K. Palagachev, Lubomira G. Softova
Abstract
Very general nonvariational elliptic equations of $p$-Laplacian type are treated. An optimal CalderónâZygmund theory is developed for such a nonlinear elliptic equation in divergence form in the setting of various function spaces including Lebesgue spaces, Orlicz spaces, weighted Orlicz spaces, and variable exponent Lebesgue spaces. The addressed arguments also apply to Morrey spaces, Lorentz spaces and generalized Orlicz spaces.
Topics & Concepts
MathematicsLp spaceLebesgue's number lemmaBirnbaum–Orlicz spaceLebesgue integrationMathematical analysisInterpolation spacePure mathematicsNonlinear systemMaximal functionFunction spaceDivergence (linguistics)Lorentz transformationFunctional analysisIntegral equationBanach spaceRiemann integralSingular integralChemistryPhysicsPhilosophyLinguisticsQuantum mechanicsClassical mechanicsGeneBiochemistryAdvanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsAdvanced Mathematical Physics Problems