S. Koike, Semicontinuous viscosity solutions for HamiltonJacobi equations with a degenerate coefficient, Differential Integral Equation., 10 (1997), 455-472. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On A Degenerate Hamilton-Jacobi Equation And A Related Topic - Strömberg (Correct)
....regards (3) 4) the continuity assumption f 2 C( 0; T ] may be relaxed so as to allow for unbounded coefficients f . Remark 2. This paper can be viewed as a continuation of [10, 11] Remark 3. Degenerate equations of the form f(x)u 0 t (t; x) H(u 0 x (t; x) 0 have been examined in [7]. ....
S. Koike, Semicontinuous viscosity solutions for Hamilton--Jacobi equations with a degenerate coefficient , Differential Integral Equations 10 (1997), 455--472.
Uniqueness of Lower Semicontinuous Viscosity Solutions.. - Alvarez, Koike, Nakayama Self-citation (Koike) (Correct)
.... Barles convolution. With this idea, Soravia [S1] studied the Dirichlet type problems. More precisely, he imposed a subsolution property on the boundary of the target, under which the uniqueness of lsc viscosity solutions for the (transformed) minimum time problem was obtained. See also [K] and [BL] for related topics. Recently, Carja et al. in [CMP] see also [C] studied lsc viscosity solutions of the minimum time problem assuming that they converge to the Dirichlet data from inside. For the viscosity solution theory of first order Hamilton Jacobi equations, we refer to a new book ....
....for the reader s convenience. Since (4.3) can be obtained easily by remarking the sign of the power on e, we shall only show (4.2) See also our proof for (4.2) below. Let us recall the Barron Jensen lemma, which will be needed also for checking the sign of q in (4.2) Lemma 4.1. See [BJ1] or [K]) Fix (x; t) 2 R n Theta (0; T ) and (p; q) 2 D u ffl (x; t) For any ff 0, there exist (x ff k ; t ff k ) 2 R n Theta (0; T ) p ff k ; q ff k ) 2 D Gamma u ffl (x ff k ; t ff k ) for k 2 f1; 2; Delta Delta Delta ; n(ff)g (with some n(ff) 2 N) x ff ; t ff ) 2 R ....
S. Koike, Semicontinuous viscosity solutions for HamiltonJacobi equations with a degenerate coefficient, Differential Integral Equation., 10 (1997), 455-472.
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