Sufficient conditions for the existence of viscosity solutions for nonconvex Hamiltonians
We study a sufficient geometric condition for the existence of a $W^{1,\infty}(\Omega)$ viscosity solution of the Hamilton--Jacobi equation $$ \left\{ \begin{array}{@{}r@{\;}c@{\;}lcc} F(Du) & = & 0 & \mbox{in} & \Omega, \\[2pt] u & = & \varphi & \mbox{on} & \partial\...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2004-01, Vol.36 (1), p.186-203 |
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| creator | PISANTE, Giovanni |
| description | We study a sufficient geometric condition for the existence of a $W^{1,\infty}(\Omega)$ viscosity solution of the Hamilton--Jacobi equation $$ \left\{ \begin{array}{@{}r@{\;}c@{\;}lcc} F(Du) & = & 0 & \mbox{in} & \Omega, \\[2pt] u & = & \varphi & \mbox{on} & \partial\Omega, \end{array} \right. $$ where $\Omega \subset {\mathbb R}^n$ and $F:{\mathbb R}^n\to {\mathbb R}$ are not necessarily convex. |
| doi_str_mv | 10.1137/S0036141003426902 |
| format | Article |
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| identifier | ISSN: 0036-1410 |
| ispartof | SIAM journal on mathematical analysis, 2004-01, Vol.36 (1), p.186-203 |
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| language | eng |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Calculus of variations and optimal control Classical and quantum physics: mechanics and fields Classical mechanics of discrete systems: general mathematical aspects Control theory Exact sciences and technology Hypotheses Mathematical analysis Mathematics Nonlinear equations Physics Sciences and techniques of general use Viscosity |
| title | Sufficient conditions for the existence of viscosity solutions for nonconvex Hamiltonians |
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