Search results for "Potential theory"

showing 4 items of 24 documents

Quasi-Continuous Vector Fields on RCD Spaces

2021

In the existing language for tensor calculus on RCD spaces, tensor fields are only defined $\mathfrak {m}$ -a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.

Quasi-continuityPure mathematics01 natural sciencesPotential theoryTensor fielddifferentiaaligeometria010104 statistics & probabilityRCD spacesSettore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsMathematicsFunctional analysisDifferential calculus; Quasi-continuity; RCD spaces010102 general mathematicsRCD spaceFunctional Analysis (math.FA)Mathematics - Functional AnalysisSobolev spaceDifferential calculusdifferential calculusVector fieldTensor calculusfunktionaalianalyysiquasi-continuityAnalysis
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Trace and density results on regular trees

2019

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

Trace (linear algebra)Mathematics::Analysis of PDEsBoundary (topology)01 natural sciencesMeasure (mathematics)Potential theorySet (abstract data type)Combinatoricsregular treeMathematics - Metric Geometry0103 physical sciencesEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsdensityMathematics::Functional Analysis010102 general mathematicsMetric Geometry (math.MG)Functional Analysis (math.FA)Sobolev spaceMathematics - Functional AnalysisMathematics - Classical Analysis and ODEs010307 mathematical physicsTree (set theory)46E35 30L99funktionaalianalyysiAnalysisboundary traceNewtonian space
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Singular Neumann (p, q)-equations

2019

We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.

TruncationGeneral MathematicsResonant nonlinearity0211 other engineering and technologies02 engineering and technology01 natural sciencesPotential theoryTruncation and comparisonTheoretical Computer ScienceSettore MAT/05 - Analisi MatematicaNeumann boundary conditionApplied mathematics0101 mathematics(p q)-equationNonlinear regularityMathematicsParametric statistics021103 operations research010102 general mathematicsSingular termSingular termMathematics::Spectral TheoryOperator theoryTerm (time)Nonlinear systemNonlinear strong maximum principleAnalysisPositivity
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Variational parabolic capacity

2015

We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.

p-parabolic equationcapacityApplied Mathematicsta111Mathematical analysisDegenerate energy levelsMathematics::Analysis of PDEsContext (language use)Parabolic cylinder functionType (model theory)Parabolic partial differential equationHeat capacityNonlinear systemdegenerate parabolic equationsnonlinear potential theoryDiscrete Mathematics and CombinatoricsAnalysisComputer Science::Information TheoryMathematicsDiscrete and Continuous Dynamical Systems
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