2001 | OriginalPaper | Buchkapitel
The Classical Maximum Principle
verfasst von : David Gilbarg, Neil S. Trudinger
Erschienen in: Elliptic Partial Differential Equations of Second Order
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The purpose of this chapter is to extend the classical maximum principles for the Laplace operator, derived in Chapter 2, to linear elliptic differential operators of the form 3.1$$ Lu = {a^{{ij}}}(x){D_{{ij}}}u + {b^i}(x){D_i}u + c(x)u, {a^{{ij = }}}{a^{{ji}}} $$, where x = (x1,..., xn) lies in a domain Ω of ℝn, n≥2. It will be assumed, unless otherwise stated, that u belongs to C2(Ω). The summation convention that repeated indices indicate summation from 1 to n is followed here as it will be throughout. L will always denote the operator (3.1).