6533b827fe1ef96bd1287259
RESEARCH PRODUCT
Removable singularities for div v=f in weighted Lebesgue spaces
Laurent MoonensHeli TuominenEmmanuel Russsubject
General Mathematics[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]Characterization (mathematics)[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencesMeasure (mathematics)functional analysisCombinatoricsMathematics - Analysis of PDEsWeightsRemovable setsClassical Analysis and ODEs (math.CA)FOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Hausdorff measure0101 mathematicsLp spaceMathematicsremovable singularities010102 general mathematicsta111Divergence operatorMSC 2010: 28A12 42B37Functional Analysis (math.FA)Mathematics - Functional AnalysisMathematics - Classical Analysis and ODEsGravitational singularityweighted Lebesgue spacesfunktionaalianalyysiAnalysis of PDEs (math.AP)description
International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |