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This is a Quantitative Study study.

October 16, 2025Open Access

Uniform estimates for elliptic equations with Caratheodory nonlinearities at the interior and on the boundary

Key Points

Weak solutions exhibit explicit uniform estimates concerning both interior and boundary nonlinearities.
The estimates are derived using a De Giorgi-Nash-Moser iterative scheme, yielding insights into elliptic regularity.
Combining different mathematical techniques, the research provides a structured method to obtain a priori estimates.
Applications of the Gagliardo-Nirenberg interpolation inequality enhance understanding of various elliptic problems.

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^ () \) a priori estimates are in terms of powers of their \ (H¹ () \) norms. To prove our result, we combine a De Giorgi-Nash-Moser iteration scheme together with elliptic regularity and the Gagliardo-Nirenberg interpolation inequality. For more information and the latex file, see https: //ejde. math. txstate. edu/Volumes/2025/95/abstr. html

Uniform estimates for elliptic equations with Caratheodory nonlinearities at the interior and on the boundary

Key Points

Abstract

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