Advances in Differential Equations

Hopf-Lax type formula for sub- and supersolutions

Adimurthi and G. D. Veerappa Gowda

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the continuous as well as discontinuous viscosity solutions of a certain Hamilton-Jacobi equation, $u_t + H(u, D u)=0$ in $\mathbb R^{\,n} \times \mathbb R_+$ with $u(x,0)=u_0(x)$. We obtain explicit formulas for continuous as well as for the sub- and supersolutions. In the latter case, furthermore, if $ H(u,p) > 0 $ for $|p| \neq 0 $ then the supersolution becomes a solution.

Article information

Source
Adv. Differential Equations Volume 5, Number 1-3 (2000), 97-119.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651380

Mathematical Reviews number (MathSciNet)
MR1734538

Zentralblatt MATH identifier
0987.35034

Subjects
Primary: 35F25: Initial value problems for nonlinear first-order equations
Secondary: 35K90: Abstract parabolic equations 35L55: Higher-order hyperbolic systems

Citation

Adimurthi; Veerappa Gowda, G. D. Hopf-Lax type formula for sub- and supersolutions. Adv. Differential Equations 5 (2000), no. 1-3, 97--119. https://projecteuclid.org/euclid.ade/1356651380.


Export citation