arXiv subjects

Edgar Antonio

Publications and source records attributed to Edgar Antonio.

2 recordsLinked to original sources

arXiv2026

$L^\infty$ estimates for solutions to elliptic equations in the presence of gradient terms

We consider an elliptic problem with slightly subcritical nonlinearities at the interior and on the boundary; the nonlinearity at the interior is also depending on a gradient term. For any $u$ weak solution, we provide explicit $L^\infty$ {\it a priori} estimates depending only on both nonlinearities, on the $H^1(\Omega)$ norm of $u,$ and on the domain $\Omega$. To obtain our results, we combine De Giorgi-Nash-Moser iteration procedure, elliptic regularity when the gradient term appears, Lebesgue interpolation and the Gagliardo-Nirenberg interpolation inequalities.

math.AP↗

arXiv2025

Uniform estimates for elliptic equations with Carath\'eodory 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 $L^{\infty}(\Omega )$ a priori estimates are in terms of powers of their $H^{1}(\Omega )$ 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↗