arXiv subjects

Jorge Sánchez Ortiz

Publications and source records attributed to Jorge Sánchez Ortiz.

2 recordsLinked to original sources

arXiv2025

Uniform estimates for elliptic equations with Carathéodory nonlinearities at the interior and on the boundary

We establish an explicit uniform a priori estimate for weak solutions to slightly subcritical elliptic problems with nonlinearities simultaneously at the interior and on the boundary. Our explicit $L^{\infty}(Ω)$ a priori estimates are in terms of powers of their $H^{1}(Ω)$ norms. To prove our result, we combine a De Giorgi-Nash-Moser's iteration scheme together with elliptic regularity and the Gagliardo-Nirenberg's interpolation inequality.

math.AP↗

arXiv2020

On a Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions in $\mathbb{R}^m$

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space $\mathbb{R}^m$. We approach this problem using the language of Clifford analysis for obtaining the explicit expression of the solution of the problem in a Jordan domain $Ω\subset\mathbb{R}^m$ with fractal boundary. One of the remarkable feature in this study is that the boundary data involves higher order Lipschitz class of functions.

math.AP↗