Search results for " 46E35"

showing 4 items of 24 documents

Local maximal operators on fractional Sobolev spaces

2016

In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …

Trace spaceFunction spaceGeneral MathematicsOpen setSpace (mathematics)01 natural sciencesDomain (mathematical analysis)CombinatoricsHardy inequality0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsfractional Sobolev spaceMathematicsMathematics::Functional Analysista111010102 general mathematicsMathematical analysis42B25 46E35 47H99Functional Analysis (math.FA)Mathematics - Functional AnalysisSobolev spaceSection (category theory)Mathematics - Classical Analysis and ODEsBounded function47H99010307 mathematical physics42B25local maximal operator

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Testing the Sobolev property with a single test plan

2020

We prove that in a vast class of metric measure spaces (namely, those whose associated Sobolev space is separable) the following property holds: a single test plan can be used to recover the minimal weak upper gradient of any Sobolev function. This means that, in order to identify which are the exceptional curves in the weak upper gradient inequality, it suffices to consider the negligible sets of a suitable Borel measure on curves, rather than the ones of the $p$-modulus. Moreover, on $\sf RCD$ spaces we can improve our result, showing that the test plan can be also chosen to be concentrated on an equi-Lipschitz family of curves.

differentiaaligeometriaMathematics - Functional AnalysisMathematics - Metric GeometryGeneral MathematicsFOS: MathematicsMetric Geometry (math.MG)RCD space53C23 46E35Sobolev spacetest planfunktionaalianalyysiComputer Science::DatabasesFunctional Analysis (math.FA)

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Fractional Maximal Functions in Metric Measure Spaces

2013

Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

fractional sobolev spacePure mathematicsQA299.6-433Applied MathematicsMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsSpace (mathematics)Lipschitz continuityMeasure (mathematics)Functional Analysis (math.FA)Sobolev spaceMathematics - Functional Analysiscampanato space42B25 46E35metric measure spaceMetric (mathematics)FOS: Mathematicsfractional maximal function46e35Maximal functionGeometry and Topology42b25AnalysisMathematicsAnalysis and Geometry in Metric Spaces

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Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

2022

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz-Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.

sub-supersolutionMathematics - Analysis of PDEsOrlicz-Sobolev spaceSettore MAT/05 - Analisi Matematicagradient dependenceGeneral Mathematicsnonlinear elliptic equationFOS: Mathematics35J25 35J99 46E35Analysis of PDEs (math.AP)

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