## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Geometry and Partial Differential Equations. Leon Simon and Neil S. Trudinger, eds. Proceedings of the Centre for Mathematical Analysis, v. 10. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1986), 177 - 186

### Some fully non-linear parabolic partial differential equations

#### Abstract

In this paper I wish to discuss the classical solvability of the first boundary value problem for a class of non-linear parabolic equations of second order. The equations to be considered arise from symmetric functions in a natural way analagous to the equations considered by Caffarelli, Nirenberg and Spruck [CNS] in the elliptic case. They are also motivated by the proposed analogue of the Monge-Ampère equation of Krylov [KL which is considered here as a first special case. I do not present the proofs of the results described, but only rough indications of the methods involved. The work constitutes the central results of the latter half of my doctoral dissertation [R l]

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416336689

**Mathematical Reviews number (MathSciNet)**

MR857666

**Zentralblatt MATH identifier**

0599.35082

#### Citation

Reye, S.J. Some fully non-linear parabolic partial differential equations. Miniconference on Geometry and Partial Differential Equations, 177--186, Centre for Mathematical Analysis, The Australian National University, Canberra AUS, 1986. https://projecteuclid.org/euclid.pcma/1416336689