Riesz Potential Equations in Local Lp-spaces.
2009 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 54, no 2, 125-151 p.Article in journal (Refereed) Published
We consider the following equation for the Riesz potential of order one:
Uniqueness of solutions is proved in the class of solutions for which the integral is absolutely convergent for almost every x. We also prove anexistence result and derive an asymptotic formula for solutions near the origin.Our analysis is carried out in local Lp-spaces and Sobolev spaces, which allows us to obtain optimal results concerning the class of right-hand sides and solutions. We also apply our results to weighted Lp-spaces and homogenous Sobolev spaces.
Place, publisher, year, edition, pages
2009. Vol. 54, no 2, 125-151 p.
Riesz potentials, Singular integral operators
IdentifiersURN: urn:nbn:se:liu:diva-16496DOI: 10.1080/17476930802669728OAI: oai:DiVA.org:liu-16496DiVA: diva2:158259