A limiting case in partial regularity for quasiconvex functionals

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]{\,{{\rm{d}}}x} $ feature almost everywhere $ \mbox{BMO} $-regular gradient provided that $ f $ belongs to the borderline Marcinkiewicz space $ L(n, \infty) $.

Keywords

• regularity
• quasiconvex functionals
• degenerate variational integrals