Maximum principle for fully nonlinear equations via the iterated comparison function method

Shigeaki Koike, Andrzej Świȩch

研究成果: Article

22 引用 (Scopus)

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We present various versions of generalized Aleksandrov-Bakelman-Pucci (ABP) maximum principle for L p -viscosity solutions of fully nonlinear second-order elliptic and parabolic equations with possibly superlinear-growth gradient terms and unbounded coefficients. We derive the results via the "iterated" comparison function method, which was introduced in our previous paper (Koike and Świȩch in Nonlin. Diff. Eq. Appl. 11, 491-509, 2004) for fully nonlinear elliptic equations. Our results extend those of (Koike and Świȩch in Nonlin. Diff. Eq. Appl. 11, 491-509, 2004) and (Fok in Comm. Partial Diff. Eq. 23(5-6), 967-983) in the elliptic case, and of (Crandall et al. in Indiana Univ. Math. J. 47(4), 1293-1326, 1998; Comm. Partial Diff. Eq. 25, 1997-2053, 2000; Wang in Comm. Pure Appl. Math. 45, 27-76, 1992) and (Crandall and Świȩch in Lecture Notes in Pure and Applied Mathematics, vol. 234. Dekker, New York, 2003) in the parabolic case.

元の言語English
ページ(範囲)461-484
ページ数24
ジャーナルMathematische Annalen
339
発行部数2
DOI
出版物ステータスPublished - 2007 10 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

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