Search results for "49L25"

showing 2 items of 2 documents

A continuous time tug-of-war game for parabolic $p(x,t)$-Laplace type equations

2019

We formulate a stochastic differential game in continuous time that represents the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the normalized $p(x,t)$-Laplace operator. Our game is formulated in a way that covers the full range $1<p(x,t)<\infty$. Furthermore, we prove the uniqueness of viscosity solutions to our equation in the whole space under suitable assumptions.

050208 financeLaplace transformApplied MathematicsGeneral MathematicsTug of warProbability (math.PR)010102 general mathematics05 social sciencesMathematical analysisType (model theory)01 natural sciencesParabolic partial differential equationTerminal valueMathematics - Analysis of PDEs0502 economics and businessDifferential gameFOS: Mathematics91A15 49L25 35K650101 mathematicsViscosity solutionMathematics - ProbabilityAnalysis of PDEs (math.AP)Mathematics
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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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