Open AccessRemarks on nonlinear uniformly parabolic equations
Author(s) -
Michael G. Crandall,
Ken Fok,
Maciej Kocan,
Andrzej Święch
Publication year - 1998
Publication title -
indiana university mathematics journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.317
H-Index - 69
eISSN - 1943-5258
pISSN - 0022-2518
DOI - 10.1512/iumj.1998.47.1561
Subject(s) - mathematics , nonlinear system , mathematical analysis , parabolic partial differential equation , partial differential equation , physics , quantum mechanics
This paper provides a number of working tools for the discussion of fully nonlinearparabolic equations. These include: a proof that the maximum principle whichprovides L1estimates of "strong" solutions of extremal equations by Ln+1normsof the forcing term over the "contact set" remains valid for viscosity solutions in anLn+1sense, a gradient estimate in Lpfor p ! (n+ 1)(n + 2) for solutions of extremalequations with forcing terms in Ln+1, the use of this estimate in...
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