Partial Regularity for Local Minimizers of Variational Integrals With Lower-Order Terms
Partial Regularity for Local Minimizers of Variational Integrals With Lower-Order Terms
We consider functionals of the form $$\mathcal{F}(u):=\int_\Omega\!F(x,u,\nabla u)\,\mathrm{d} x,$$ where $\Omega\subseteq\mathbb{R}^n$ is open and bounded. The integrand $F\colon\Omega\times\mathbb{R}^N\times\mathbb{R}^{N\times n}\to\mathbb{R}$ is assumed to satisfy the classical assumptions of a power $p$-growth and the corresponding strong quasiconvexity. In addition, $F$ is H\"older continuous with exponent $2\beta\in(0,1)$ in its first two variables uniformly …