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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

Generalize Solution Dirichlet Problem Elliptic Operator Uniqueness Theorem Unique Solvability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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