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.
Citation
Adimurthi. G. D. Veerappa Gowda. "Hopf-Lax type formula for sub- and supersolutions." Adv. Differential Equations 5 (1-3) 97 - 119, 2000. https://doi.org/10.57262/ade/1356651380
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