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

• 小池, 茂昭

抄録

type:text

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 Swiech in Nonlin. Diff. Eq. Appl. 11, 491-509, 2004) for fully nonlinear elliptic equations. Our results extend those of (Koike and Swiech 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 Swiech in Lecture Notes in Pure and Applied Mathematics, vol. 234. Dekker, New York, 2003) in the parabolic case.

Copyright notice(c)2007 Springer. All rights reserved. Publisher's version: http://www.springerlink.com/content/q2116t16t16x6132/

収録刊行物

• MATHEMATISCHE ANNALEN

  MATHEMATISCHE ANNALEN 339 (2), 461-484, 2007

  SPRINGER

詳細情報

• CRID: 1050564287771434624
• NII論文ID: 120006385615
• ISSN: 00255831
• Web Site: http://id.nii.ac.jp/1586/00013123/
• 本文言語コード: en
• 資料種別: journal article
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