Search results for "subelliptic equations."

showing 2 items of 2 documents

Convex functions on Carnot Groups

2007

We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.

Convex analysisPure mathematicsCarnot groupsubelliptic equations.49L25Mathematics::Complex VariablesGeneral MathematicsMathematical analysissubelliptic equationsMathematics::Analysis of PDEsHorizontal convexityviscosity convexity35J70Convexitysymbols.namesakeCarnot groupsHomogeneous35J67Convex optimizationsymbolsPoint (geometry)Carnot cycleConvex function22E30Mathematics
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C1,α-regularity for variational problems in the Heisenberg group

2017

We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.

osittaisdifferentiaaliyhtälötNumerical AnalysisregularityHeisenberg groupsApplied Mathematicsp-Laplacian010102 general mathematicsScalar (mathematics)subelliptic equationsHölder condition01 natural sciences35H20 35J70010101 applied mathematicsMaxima and minimaMathematics - Analysis of PDEsweak solutionsPhysics::Atomic and Molecular Clustersp-LaplacianHeisenberg group0101 mathematicsAnalysisMathematical physicsMathematicsAnalysis &amp; PDE
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