A Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. II

Authors:
Y. S. Choi and P. J. McKenna

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2925-2937

MSC (1991):
Primary 35J25

DOI:
https://doi.org/10.1090/S0002-9947-98-02276-4

MathSciNet review:
1491858

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let with . We consider the equations

with and . We show that if is a convex bounded region in , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for non-convex domains in are also given.

**1.**S. Canic and B. L. Keyfitz,*An elliptic problem arising form the unsteady transonic small disturbance equation*, J. Diff. Eqs. 125 (1996), 548-574. MR**97c:35073****2.**Y. S. Choi, A.C. Lazer, and P. J. McKenna,*On a singular quasilinear anisotropic elliptic boundary value problem*, Trans. A.M.S., 347 (1995), pp. 2633-2641. MR**95i:35087****3.**M.G.Crandall, P. H. Rabinowitz, and L. Tartar,*On a Dirichlet problem with a singular nonlinearity*, Comm. P.D.E.,2(2), (1977) 193-222. MR**55:856****4.**D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. 2nd edition, (1983) Springer-Verlag. MR**86c:35035****5.**A. C. Lazer and P. J. McKenna,*On a singular nonlinear elliptic boundary value problem*, Proceedings of the AMS, 111, (1991) 721-730. MR**91f:35099****6.**A. Nachman and A. Callegari,*A nonlinear singular boundary value problem in the theory of pseudoplastic fluids*, SIAM J. Appl. Math. 28 (1986), 271-281. MR**81e:76003****7.**W. Reichel,*Uniqueness for degenerate elliptic equations via Serrin's sweeping principle*, General Inequalities 7, International Series of Numerical Mathematics, Birkhäuser, Basel, 1997, pp. 375-387. CMP**97:14****8.**D.H. Sattinger, Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, no. 309, Springer-Verlag, 1973. MR**57:3569****9.**C.A. Stuart,*Existence theorems for a class of nonlinear integral equations*, Math. Z., 137 (1974), 49-66. MR**50:914****10.**S.D. Taliaferro,*A nonlinear singular boundary value problem*, Nonlinear Analysis, T.M.A. 3 (1979), 897-904. MR**81i:34011**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
35J25

Retrieve articles in all journals with MSC (1991): 35J25

Additional Information

**Y. S. Choi**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268

Email:
choi@math.uconn.edu

**P. J. McKenna**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268

Email:
mckenna@math.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-02276-4

Keywords:
Harnack inequality,
singular,
subsolution,
supersolution

Received by editor(s):
August 6, 1996

Article copyright:
© Copyright 1998
American Mathematical Society