4 papers
A critical Hardy-Rellich inequality
Hernán Castro
In this work, we prove a critical version of a Hardy-Rellich type inequality. We show that for and for , there exists a constant such that \…
Interior regularity of some weighted quasi-linear equations
Hernán 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 }Ω,\\ u\in H^{1,p}_{loc}&…
Interior regularity of doubly weighted quasi-linear equations
Hernán Castro
In this article we study the quasi-linear equation \[\mathrm{div}\, \mathcal A(x,u,\nabla u)=\mathcal B(x,u,\nabla u)\quad \text{in }Ω,\qquad u\in H^{1,p}_{loc}(Ω;w_1dx)\] where…
theory for a singular Sturm-Liouville equation
Hernán Castro, Iván Proaño
In this paper we consider the following Sturm-Liouville equation \[ \left\{ \begin{aligned} -(x^{2α}u'(x))'+u(x)&=f(x) && \text{in } (0,1],\\ u(1)&=0 \end{aligned} \right. \] wher…