Parabolic systems with polynomial growth and regularity
Frank Duzaar, Giuseppe Mingione, Klaus Steffen
The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here
Kategorije:
Godina:
2011
Izdavač:
Amer Mathematical Society
Jezik:
english
Strane:
135
ISBN 10:
0821849670
ISBN 13:
9780821849675
Serije:
Memoirs of the American Mathematical Society 1005
Fajl:
PDF, 968 KB
IPFS:
,
english, 2011