Edgar Antonio, Martin P. Arciga-Alejandre, Rosa Pardo, Jorge Sanchez-Ortiz
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 iteration scheme together with elliptic regularity and the
Gagliardo-Nirenberg interpolation inequality.
Submitted January 24, 2025. Published October 13, 2025.
Math Subject Classifications: 35B45, 35J66, 35B33, 35J75, 35J25
Key Words: A priori estimates; slightly subcritical non-linearities; L-infinity a priori bounds;
nonlinear boundary conditions.
DOI: 10.58997/ejde.2025.95
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Edgar Antonio Universidad Autónoma de Guerrero Guerrero, México email: eaam020713@gmail.com |
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Martín P. Árciga-Alejandre Universidad Autónoma de Guerrero Guerrero, México email: mparciga@uagro.mx |
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Rosa Pardo Universidad Complutense de Madrid Madrid, Spain email: rpardo@ucm.es |
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Jorge Sánchez-Ortiz Universidad Autónoma de Guerrero Guerrero, México email: jsanchez@uagro.mx |
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