6533b854fe1ef96bd12aec63
RESEARCH PRODUCT
A DUALITY APPROACH TO THE FRACTIONAL LAPLACIAN WITH MEASURE DATA
Francesco PetittaKenneth H. KarlsenSuleyman Ulusoysubject
Pure mathematicsGeneral MathematicsDuality (optimization)fractional laplacianmeasure dataExistenceMeasure (mathematics)Duality solutionsFractional LaplacianOrder (group theory)UniquenessMeasure dataMathematicsFractional Laplacian ; Measure data ; Existence ; Uniqueness ; Duality solutions35B40Mathematical analysisexistenceuniquenessduality solutionsBounded function35K55Radon measurefractional laplacian; uniqueness; duality solutions; measure data; existenceUniquenessFractional LaplacianLaplace operatordescription
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$(-\Delta)^s v = \mu \quad \text{in } \mathbb{R}^N,$$ ¶ with vanishing conditions at infinity. Here $\mu$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(\Delta)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 |