Maximal Function Methods for Sobolev Spaces
Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas
Abstract
Maximal functions -- Lipeschitz and Sobolev functions -- Sobolev and Poincaré inequalities -- Pointwise inequalities for Sobolev functions -- Capacities and fine properties of Sobolev functions -- Hardy's inequalities -- Density conditions -- Muckenhoupt weights -- Weighted maximal and Poincaré inequalities -- Distance weights and Hardy-Sobolev inequalities -- The p-Laplace equation -- Stability results for the p-Laplace equation
Topics & Concepts
Sobolev spaceInterpolation spaceFunction spaceFunction (biology)MathematicsPure mathematicsFunctional analysisBiologyBiochemistryEvolutionary biologyGeneNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems