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arXiv · 2502.14609

Uniform estimates for elliptic equations with Carath\'eodory nonlinearities at the interior and on the boundary

Edgar Antonio·Martín P. Árciga-Alejandre·Rosa Pardo·Jorge Sánchez Ortiz
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Abstract

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.

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Edgar Antonio, Martín P. Árciga-Alejandre, Rosa Pardo, Jorge Sánchez Ortiz. 2025-02-20. Uniform estimates for elliptic equations with Carath\'eodory nonlinearities at the interior and on the boundary. https://arxiv.org/abs/2502.14609

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