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An Aleksandrov-Bakelman Type Maximum Principle and Applications

✍ Scribed by Y.S. Luo

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
509 KB
Volume
101
Category
Article
ISSN
0022-0396

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✦ Synopsis

We prove various local estimates for solutions of linear elliptic equations of second order with Venttsel boundary conditions. These estimates include boundary versions of maximum principles of Aleksandrov and Bakelman and weak Harnack inequalities which are fundamental for HΓΆlder estimates for solutions of nonlinear Venttsel boundary value problems. / 1993 Academic Press. Inc.

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We consider an abstract linear elliptic boundary value problem Au y u s yf Ε½ . y 1 F0 in a strongly ordered Banach space X. The resolvent I y A of the closed linear operator A : X Βͺ X is assumed to be strongly positive and compact for all ) , where denotes the principal eigenvalue of A.