On analyticity in homogeneous first order partial differential equations
On Boolean partial differential equations
On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes
On the existence of global holomorphic solutions of differential equations with complex parameters
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the solvability of the equation div in and in
We show that the equation div has, in general, no Lipschitz (respectively ) solution if is (respectively ).