Regularity of Keldys-Fichera boundary value problem for degenerate elliptic equations

Abstract

The authors discuss the W ^1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle, the reversed Hölder inequality and the generalized poincaré inequalities.

Keywords

Keldys-Fichera boundary value problem / W ^1,p-regularity / Interior regularity

References

[1] Adams R. A.. Sobolev Space, 1975, New York: Academic Press

[2] Chen Z. C.. The Keldys-Fichera boundary value problem for a class of nonlinear degenerate elliptic equations. Acta Math. Sin., New Series, 1993, 9(2): 203-211

[3] Chen Z. C., Xuan B. J.. On the Keldys-Fichera boundary value problem for degenerate quasilinear elliptic equations. Electron. J. Diff. Eqs., 2002, 87: 1-13

[4] Gilbarg D., Trudinger N. S.. Elliptic Partial Differential Equations of Second Order, 1977, New York: Springer-Verlag

[5] Ladyzenskaja O. A., Uralceva N. N.. Linear and Quasilinear Equations of Elliptic Type (in Russian), 1973, Moscow: Science Press

[6] Li S. H.. The first boundary value problem for quasilinear ellptic-parabolic equation with double degenerate. Nonlinear Anal., Theor., Meth. Appl., 1996, 27(1): 115-124

[7] Ma T., Yu Q. Y.. The Keldys-Fichera boundary value problems for degenerate quasilinear elliptic equations of second order. Diff. Int. Eqn., 1989, 2: 379-388

[8] Oleinik O. A., Radkevic E. V.. Second Order Equation with Nonnegative Characteristic Form, 1973, New York: AMS Rhode Island and Plennum Press

[9] Temam R.. Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 1988, New York: Springer-Verlag

[10] Wang L. H.. Hölder estimates for subelliptic operators. J. Funct. Anal., 2003, 199: 228-242