A limiting case in partial regularity for quasiconvex functionals

Mirco Piccinini

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arXiv · 2308.05446

A limiting case in partial regularity for quasiconvex functionals

Mirco Piccinini

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Abstract

Local minimizers of nonhomogeneous quasiconvex variational integrals with standard $p$-growth of the type $$ w \mapsto \int \left[F(Dw)-f\cdot w\right]dx $$ feature almost everywhere $\mbox{BMO}$-regular gradient provided that $f$ belongs to the borderline Marcinkiewicz space $L(n,\infty)$.

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Mirco Piccinini. 2023-08-10. A limiting case in partial regularity for quasiconvex functionals. https://arxiv.org/abs/2308.05446

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