Partial regularity for parabolic systems with VMO-coefficients
The author studies the regularity properties of the solutions of the following parabolic system in divergence form \[ u_t-\mathrm{div} A(x,t,u,Du)=0 \qquad \text{ in } \Omega_T=\Omega\times(-T,0)) \] It is established a partial Hölder regularity result for the weak solutions imposing standard \(p\)-growth condition and ellipticity condition on the principal operator. The vector-function \(A\) is discontinuous in \((x,t)\) verifying a VMO-type condition. The parabolic structure of the operator requires the use of suitable intrinsic cylinders that permit to apply the method of \(\mathcal{A}\)-caloric approximation.
scientific article; zbMATH DE number 7359968
scientific article