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

MathSciNet review:
871676

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

**[1]**George 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****[2]**David Gilbarg and Lars Hörmander,*Intermediate Schauder estimates*, Arch. Rational Mech. Anal.**74**(1980), no. 4, 297–318. MR**588031**, 10.1007/BF00249677**[3]**David Gilbarg and Neil S. Trudinger,*Elliptic partial differential equations of second order*, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR**737190****[4]**Enrico Giusti,*Boundary behavior of non-parametric minimal surfaces*, Indiana Univ. Math. J.**22**(1972/73), 435–444. MR**0305253****[5]**Gary M. Lieberman,*The quasilinear Dirichlet problem with decreased regularity at the boundary*, Comm. Partial Differential Equations**6**(1981), no. 4, 437–497. MR**612553**, 10.1080/03605308108820184**[6]**Gary M. Lieberman,*The Dirichlet problem for quasilinear elliptic equations with Hölder continuous boundary values*, Arch. Rational Mech. Anal.**79**(1982), no. 4, 305–323. MR**656797**, 10.1007/BF00250796**[7]**Gary M. Lieberman,*Regularized distance and its applications*, Pacific J. Math.**117**(1985), no. 2, 329–352. MR**779924****[8]**Gary M. Lieberman,*The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data*, Comm. Partial Differential Equations**11**(1986), no. 2, 167–229. MR**818099**, 10.1080/03605308608820422**[9]**Gary M. Lieberman and Neil S. Trudinger,*Nonlinear oblique boundary value problems for nonlinear elliptic equations*, Trans. Amer. Math. Soc.**295**(1986), no. 2, 509–546. MR**833695**, 10.1090/S0002-9947-1986-0833695-6**[10]**J. D. Madjarova,*On the Neumann problem for a fully nonlinear convex elliptic equation*, C. R. Acad. Bulgare Sci.**38**(1985), no. 2, 183–186. MR**789129****[11]**M. V. Safonov,*On the classical solution of Bellman's elliptic equation*, Soviet Math. Dokl.**30**(1984), 482-485.**[12]**Jean E. Taylor,*Boundary regularity for solutions to various capillarity and free boundary problems*, Comm. Partial Differential Equations**2**(1977), no. 4, 323–357. MR**0487721****[13]**Neil S. Trudinger,*On an interpolation inequality and its applications to nonlinear elliptic equations*, Proc. Amer. Math. Soc.**95**(1985), no. 1, 73–78. MR**796449**, 10.1090/S0002-9939-1985-0796449-X**[14]**Guo Chun Wen,*Some nonlinear boundary value problems for nonlinear elliptic equations of second order in the plane*, Complex Variables Theory Appl.**4**(1985), no. 3, 189–204. MR**801637**

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