Partial regularity for subquadratic parabolic systems with continuous coefficients
The authors consider singular parabolic quasilinear equations of the type \[ u_t =\operatorname{div }a(x,t, u, Du) \] where \(a\) is a vector field satisfying subquadratic growth and ellipticity conditions. They only require that the coefficients of the system are continuous with respect to the first two arguments. Under these assumptions, they are able to prove that there is an open subset with full measure of the solution's domain, on which the solution is Hölder continuous. A similar result was conjectured by Campanato several years ago. In the last years, this regularity problem was faced under different assumptions, especially in the elliptic case, by several researchers, among them we quote Baroni, Boegelein, Duzaar, Mingione and Steffen. In this paper, an essential tool is the DiBenedetto's intrinsing scaling approach. Moreover, we remark that the authors adapt the classical \(A\)-caloric approximation lemma to this specific case.
scientific article; zbMATH DE number 6084031
scientific article