Hopf-Lax type formula for sub- and supersolutions

Adimurthi, Adi ; Gowda G D, Veerappa (2000) Hopf-Lax type formula for sub- and supersolutions Advances in Differential Equations, 5 (1-3). pp. 97-119. ISSN 1079-9389

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We study the continuous as well as discontinuous viscosity solutions of a certain Hamilton-Jacobi equation, ut + H(u,Du) = 0 in ℝn × ℝ+ with u(x, 0) = u0(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| ≠ 0 then the supersolution becomes a solution.

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