Two-dimensional nonlinear boundary value problems for elliptic equations

Author:
Gary M. Lieberman

Journal:
Trans. Amer. Math. Soc. **300** (1987), 287-295

MSC:
Primary 35J65; Secondary 35B65

DOI:
https://doi.org/10.1090/S0002-9947-1987-0871676-8

MathSciNet review:
871676

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Boundary regularity of solutions of the fully nonlinear boundary value problem

**[1]**G. E. Backus,*Application of a non-linear boundary-value problem for Laplace's equation to gravity and geomagnetic intensity surveys*, Quart. J. Mech. Appl. Math.**21**(1968), 195-221. MR**0227444 (37:3028)****[2]**D. Gilbarg and L. Hörmander,*Intermediate Schauder estimates*, Arch. Rational Mech. Anal.**74**(1980), 297-318. MR**588031 (82a:35038)****[3]**D. Gilbarg and N. S. Trudinger,*Elliptic partial differential equations of second order*, 2nd ed., Grundlehren Math. Wiss., Band 224, Springer-Verlag, Berlin and New York, 1983. MR**737190 (86c:35035)****[4]**E. Giusti,*Boundary behavior of non-parametric minimal surfaces*, Indiana Univ. Math. J.**22**(1972), 435-444. MR**0305253 (46:4383)****[5]**G. M. Lieberman,*The quasilinear Dirichlet problem with decreased regularity at the boundary*, Comm. Partial Differential Equations**6**(1981), 437-497. MR**612553 (83g:35032)****[6]**-,*The Dirichlet problem for quasilinear elliptic equations with Holder continuous boundary values*, Arch. Rational Mech. Anal.**79**(1982), 305-3[ill]3. MR**656797 (83j:35048)****[7]**-,*Regularized distance and its applications*, Pacific J. Math.**117**(1985), 329-352. MR**779924 (87j:35101)****[8]**-,*The Dirichlet problem for quasilinear elliptic equations with continuously differentiate boundary data*, Comm. Partial Differential Equations**11**(1986), 167-229. MR**818099 (87f:35073)****[9]**G. M. Lieberman and N. S. Trudinger,*Nonlinear oblique boundary value problems for nonlinear elliptic equations*, Trans. Amer. Math. Soc.**295**(1986), 509-546. MR**833695 (87h:35114)****[10]**J. D. Madjarova,*On the Neumann problem for a fully nonlinear convex, elliptic equation*, C. R. Acad. Bulgare Sci.**38**(1985), 183-186. MR**789129 (86g:35078)****[11]**M. V. Safonov,*On the classical solution of Bellman's elliptic equation*, Soviet Math. Dokl.**30**(1984), 482-485.**[12]**J. Taylor,*Boundary regularity for solutions to various capillarity and free boundary problems*, Comm. Partial Differential Equations**2**(1977), 323-357. MR**0487721 (58:7336)****[13]**N. S. Trudinger,*On an interpolation inequality and its application to nonlinear elliptic equations*, Proc. Amer. Math. Soc.**95**(1985), 73-78. MR**796449 (87a:35077)****[14]**G. C. Wen,*Some nonlinear boundary value problems for nonlinear elliptic equations of second order in the plane*, Complex Variables**4**(1985), 189-204. MR**801637 (86i:35053)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
35J65,
35B65

Retrieve articles in all journals with MSC: 35J65, 35B65

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0871676-8

Keywords:
Elliptic equations,
boundary value problems,
two-dimensional,
boundary regularity

Article copyright:
© Copyright 1987
American Mathematical Society