Lipschitz Bounds and Nonautonomous Integrals
Cristiana De Filippis, Giuseppe Mingione
Abstract
Abstract We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.
Topics & Concepts
Lipschitz continuityMathematicsPolynomialClass (philosophy)Exponential functionRange (aeronautics)Type (biology)Mathematical analysisApplied mathematicsLipschitz domainYield (engineering)Exponential growthExponential typeNonlinear systemComplex systemPure mathematicsUpper and lower boundsVariational analysisNonlinear Partial Differential EquationsOptimization and Variational AnalysisGeometric Analysis and Curvature Flows