## Differential and Integral Equations

- Differential Integral Equations
- Volume 15, Number 1 (2002), 47-52.

### The Hopf-Lax formula gives the unique viscosity solution

#### Abstract

It is proved that the Hopf--Lax formula provides the unique viscosity solution of the Cauchy problem \begin{align*} u'_t(t,x)+H(u'_x(t,x)) & =0, \qquad(t,x)\in(0,T]\times {\bf R}^n,\\ \lim_{t\downarrow0} u(t,x) & =\varphi(x)\qquad\text{for all $x\in {\bf R}^n$.} \end{align*}

#### Article information

**Source**

Differential Integral Equations, Volume 15, Number 1 (2002), 47-52.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060882

**Mathematical Reviews number (MathSciNet)**

MR1869821

**Zentralblatt MATH identifier**

1026.49023

**Subjects**

Primary: 49L25: Viscosity solutions

Secondary: 35F20: Nonlinear first-order equations

#### Citation

Strömberg, Thomas. The Hopf-Lax formula gives the unique viscosity solution. Differential Integral Equations 15 (2002), no. 1, 47--52. https://projecteuclid.org/euclid.die/1356060882