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The Dirichlet Problem for Second-Order Quasi-Linear Nonuniformly Elliptic Equations

  • A. V. Ivanov
Chapter
Part of the Seminars in Mathematics book series (SM)

Abstract

We wish to investigate the following equation in the bounded domain Ω < En, n ≥ π:
$${A_{ij}}\left( {x,u,{u_x}} \right){u_{ij}} = \beta \left( {x,u,{u_x}} \right),$$
(1)
in which \({A_{ij}} = {A_{ji}},{u_x} = \left( {{u_{{x_1}}}, \ldots {u_{xn}}} \right),{u_{ij}} = {u_{{x_i}{x_j}}}\). Let λ(x,u,p) and Λ (x,u,p) be the smallest and largest eigenvalues of the matrix ║ Aij (z,u,p)║, so that \(\lambda {\xi ^2} \leqslant {A_{ij}}{\xi _i}{\xi _j} \leqslant \Lambda {\xi ^2}\).

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Copyright information

© Springer Science+Business Media New York 1972

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  • A. V. Ivanov

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