Abstract
We study the generalized Keldys-Fichera boundary value problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Hölder inequalities and Young inequalities we discuss the existence of the weak solution. Then by using the inverse Hölder inequalities, we obtain the regularity of the weak solution in the anisotropic Sobolev space.
Highlights
Keldys 1 studies the boundary problem for linear elliptic equations with degenerationg on the boundary
In 1989, Ma and Yu 3 studied the existence of weak solution for the Keldys-Fichera boundary value of the nonlinear degenerate elliptic equations of second-order
We study the generalized KeldysFichera boundary value problem which is a kind of new boundary conditions for a class of higher-order equations with nonnegative characteristic form
Summary
Keldys 1 studies the boundary problem for linear elliptic equations with degenerationg on the boundary. For the linear elliptic equations with nonnegative characteristic forms, Oleinik and Radkevich 2 had discussed the Keldys-Fichera boundary value problem. In 1989, Ma and Yu 3 studied the existence of weak solution for the Keldys-Fichera boundary value of the nonlinear degenerate elliptic equations of second-order. We study the generalized KeldysFichera boundary value problem which is a kind of new boundary conditions for a class of higher-order equations with nonnegative characteristic form. Boundary Value Problems where x ∈ Ω, Ω ⊂ Rn is an open set, the coefficients of L are bounded measurable, and the leading term coefficients satisfy aαβ x ξαξβ ≥ 0. We investigate the generalized Keldys-Fichera boundary value conditions as follows: Dαu|∂Ω 0, |α| ≤ m − 2, Nm−1.
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