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arXiv · 2610.27212

A Brezis--Merle inequality for the biharmonic operator with Dirichlet boundary conditions in four-dimensional balls

João Marcos do Ó·Federica Sani·Victor Rafael Silva
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Abstract

In this paper, we establish a Brezis-Merle type inequality for very weak solutions of the biharmonic Dirichlet problem in the four-dimensional unit ball. By combining this inequality with moving-plane arguments, we obtain uniform a priori estimates for positive solutions of semilinear biharmonic equations with exponential nonlinearities in both the subcritical and critical regimes. As an application of these estimates, we prove the existence of a positive solution by means of topological methods. We also extend the analysis to a class of non-variational cooperative systems.

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João Marcos do Ó, Federica Sani, Victor Rafael Silva. 2026-10-19. A Brezis--Merle inequality for the biharmonic operator with Dirichlet boundary conditions in four-dimensional balls. https://arxiv.org/abs/2610.27212

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