Second order parabolic systems, optimal regularity, and singular sets of solutions

110 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Parabolic systems with polynomial growth and regularity (2011, methodology): “The A-caloric approximation technique, in its basic form, has been introduced in [33] in order to treat the partial regularity of solutions to parabolic systems with quadratic growth, while a higher order version of it, suitable to deal with systems depending on higher order spatial derivatives of s”
Global gradient estimates for degenerate parabolic equations in nonsmooth domains (2009, result): “See also DuzaarMingione [8] for further parabolic regularity results and [7] for the corresponding results of p-Laplacean type.”
Self-improving property of nonlinear higher order parabolic systems near the boundary (2010, background): “For recent parabolic applications of higher integrability in the framework of partial regularity and CalderónZygmund type estimates, see for example Acerbi-Mingione [4], Acerbi-MingioneSeregin [5], Bögelein [10], Duzaar-Mingione [16], Duzaar-Mingione-Steffen [17] and Bögelein-Duzaar-Mingione [11].”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, methodology): “As a final observation let me mention that when p = 2 the parabolic analogue of Theorem 4.14, and therefore of the original De Giorgi's lemma, has been obtained in [102] ; for the case p = 2 proving such a parabolic analogue remains an open problem.”