Boundedness of Solutions to Nonlocal Systems

Serena Dipierro; João Gonçalves da Silva; Giorgio Poggesi; Enrico Valdinoci

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arXiv · 2610.02810

Boundedness of Solutions to Nonlocal Systems

Serena Dipierro·João Gonçalves da Silva·Giorgio Poggesi·Enrico Valdinoci

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Abstract

Under mild mass or energy assumptions, we prove uniform $L^\infty$ bounds for all distributional solutions of a multi-dimensional system of nonlocal semilinear equations. The setting comprises Ginzburg-Landau systems and Allen-Cahn equations, and the results obtained are new even for scalar equations.

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Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi, Enrico Valdinoci. 2026-10-02. Boundedness of Solutions to Nonlocal Systems. https://arxiv.org/abs/2610.02810

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