Equations of Elliptic Type

  • O. A. Ladyzhenskaya
Part of the Applied Mathematical Sciences book series (AMS, volume 49)

Abstract

In this section we shall consider linear second-order equations
$$\begin{array}{*{20}{c}} {Lu = \sum\limits_{{i,j = 1}}^{n} {\frac{\partial }{{\partial {{x}_{i}}}}} ({{a}_{{ij}}}(x){{u}_{{{{x}_{j}}}}} + {{a}_{i}}(x)u(x))} \\ {\quad {\mkern 1mu} + \sum\limits_{{i = 1}}^{n} {{{b}_{i}}} (x){{u}_{{{{x}_{i}}}}} + a(x)u = f(x) + \sum\limits_{{i = 1}}^{n} {\frac{{\partial {{f}_{i}}(x)}}{{\partial {{x}_{i}}}}} ,\quad {{a}_{{ij}}}\left( x \right) = {{a}_{{ji}}}\left( x \right),} \\ \end{array}$$
(1.1)
with real coefficients which satisfy the condition of uniform ellipticity in a bounded domain Ω of Euclidean space R n .

Keywords

Manifold Dition 

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • O. A. Ladyzhenskaya
    • 1
  1. 1.Mathematical InstituteLeningrad D-11USSR

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