General Solution of the Inhomogeneous Div-Curl System and Consequences
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-017-0805-z
Abstract: We consider the inhomogeneous div-curl system (i.e. to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $$\mathbb {R}^3$$R3. An explicit general solution is given in terms of classical… read more here.
Keywords: general solution; curl system; div curl; solution ... See more keywords
Fractional div-curl quantities and applications to nonlocal geometric equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2018.03.016
Abstract: Abstract We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman–Lions–Meyer–Semmes to fractional div-curl quantities, obtaining, in particular, a nonlocal version of Wente's lemma. We demonstrate how these… read more here.
Keywords: harmonic maps; div curl; curl quantities; fractional div ... See more keywords
An Exterior Neumann Boundary-Value Problem for the Div-Curl System and Applications
Sign Up to like & getrecommendations! Published in 2021 at "Mathematics"
DOI: 10.3390/math9141609
Abstract: We investigate a generalization of the equation curlw→=g→ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains… read more here.
Keywords: system; curl system; problem; div curl ... See more keywords