Abstract
<abstract><p>Local minimizers of nonhomogeneous quasiconvex variational integrals with standard $ p $-growth of the type</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ w\mapsto \int \left[F(Dw)-f\cdot w\right]{\,{{\rm{d}}}x} $\end{document} </tex-math></disp-formula></p>
<p>feature almost everywhere $ \mbox{BMO} $-regular gradient provided that $ f $ belongs to the borderline Marcinkiewicz space $ L(n, \infty) $.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Mathematical Physics,Analysis
Reference42 articles.
1. E. Acerbi, N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., 86 (1984), 125–145. https://doi.org/10.1007/BF00275731
2. E. Acerbi, N. Fusco, A regularity theorem for minimizers of quasiconvex integrals, Arch. Rational Mech. Anal., 99 (1987), 261–281. https://doi.org/10.1007/BF00284509
3. E. Acerbi, G. Mingione, Regularity results for a class of quasiconvex functionals with nonstandard growth, Ann. Sc. Norm. Super. Pisa Cl. Sci., 30 (2001), 311–339.
4. J. M. Ball, F. Murat, $W^{1, p}$-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., 58 (1984), 225–253. https://doi.org/10.1016/0022-1236(84)90041-7
5. M. Bärlin, F. Gmeineder, C. Irving, J. Kristensen, $\mathcal{A}$-harmonic approximation and partial regularity, revisited, arXiv, 2022. https://doi.org/10.48550/arXiv.2212.12821