Hernán Castro

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20242026

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math.AP2026

A critical Hardy-Rellich inequality

HernÃ¡n Castro

In this work, we prove a critical version of a Hardy-Rellich type inequality. We show that for $N \geq 1$ and for $- N < a < 1$ , $a \neq = 0$ there exists a constant $C_{N, a} > 0$ such that \…

math.AP2025

Interior regularity of some weighted quasi-linear equations

HernÃ¡n Castro

In this article we study the quasi-linear equation \[ \left\{ \begin{aligned} \mathrm{div}\, \mathcal A(x,u,\nabla u)&=\mathcal B(x,u,\nabla u)&&\text{in }Î©,\\ u\in H^{1,p}_{loc}&…

math.AP2024

Interior regularity of doubly weighted quasi-linear equations

HernÃ¡n Castro

In this article we study the quasi-linear equation \[\mathrm{div}\, \mathcal A(x,u,\nabla u)=\mathcal B(x,u,\nabla u)\quad \text{in }Î©,\qquad u\in H^{1,p}_{loc}(Î©;w_1dx)\] where…