The solvability of the equation L u= f is considered for a hypocomplex vector field L in R 2.
When L satisfies a Łojasiewiczproperty, the solutions can be represented through a …

We study the Hölder solvability of a class of complex vector fields on the torus $\mathbb {T}^
2$. We make use of the Theta function to associate a Cauchy-Pompeiu type integral …

We show an approximation theorem of Runge type for solutions of the generalized Vekua
equation L u= A u+ B u¯ Lu=Au+Bu, where L belongs to a class of degenerate elliptic planar …

This paper deals with the solvability of planar complex vector fields with homogeneous
degeneracies. Hölder continuous solutions are obtained via a Cauchy type integral operator …

We discuss strong uniqueness results in the forward Cauchy Problem for a class of complex
fist-order equations with Hölder coefficients defined in the plane. We use an appropriate …

For a real analytic complex vector field $ L $ in an open set of $\mathbb {R}^ 2$, with local
first integrals that are open maps, we attach a number $\mu\ge 1$(obtained through …

In this paper we seek for (Hölder) continuous global solutions to the equation L u= f in the
plane, for f belonging to a subspace of L p (R 2), p≥ 1, where L is a degenerate elliptic …

For a real analytic complex vector field $ L $, in an open set of $\mathbb {R}^ 2$, with local
first integrals that are open maps, we attach a number $\mu\ge 1$(obtained through …

This paper deals with the solvability of planar vector fields\displaystyle L= A ∂ _x+ B ∂ _y,
with A and B complex-valued function in a domain Ω ⊂ R^ 2. We assume that L has a first …

Vamos tratar do análogo ao problema de Riemann-Hilbert para uma classe de campos
vetoriais planares elıticos degenerados. Assumimos que para cada ponto p onde o campo …