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Abdelhamid Meziani

Publications and source records attributed to Abdelhamid Meziani.

6 recordsLinked to original sources
arXiv2022

A Lojasiewicz Inequality in Hypocomplex Structures of $\mathbb{R}^2$

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 $μ\ge 1$ (obtained through Lojasiewicz inequalities) and show that the equation $Lu=f$ has bounded solutions when $f\in L^p$ with $p>1+μ$. We also establish a similarity principle between the bounded solutions of the equation $Lu=Au+B\overline{u}$ (with $A,B\in L^p$) and holomorphic functions.

math.AP↗
arXiv2021

Infinitesimal Bendings for Classes of Two Dimensional Surfaces

Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential equations with periodic coefficients.

math.AP↗
arXiv2019

Class of hypocomplex structures on the two dimensional torus

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 operator. A similarity principle for the solutions of the equation $Lu=au+b\bar{u}$ is obtained.

math.AP↗
arXiv2009

On First and Second Order Planar Elliptic Equations with Degeneracies

This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

math.AP↗