Neumann-Type Boundary Conditions for Hamilton-Jacobi Equations in Smooth Domains

By M. Day. 2006

78 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Oblique boundary value problems for augmented Hessian equations I (2015, unknown): “tisfying (4.18), since |x−z+rν(z)| ≥ rfor z∈ ∂Ω and x∈ Ω,¯ we have (4.19) ν(z) · (z−x) ≤ |z−x|2 2r , for z ∈ ∂Ω and x ∈ Ω. The geometric property (4.19) was ﬁrst observed in [25], a¯ nd later used in [10,26,27] and etc. If ˆx∈ ∂Ω, taking ξ(x) = u(y) + φ(x,y), we see that v(x) − ξ(x) attains its maxi”
Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks (2013, background): “infima) of sub-solutions are known to satisfy boundary conditions in a viscosity sense [22, 8].”
An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications (2013, background): “We refer to Crandall et al. [21] or Lions [36] for a complete proof.”
On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions (2011, unknown): “ion of (CN) or (DBC) with u0 = uk 0 for a suitable large M1 >0. We can easily see that uk ± are a sub and supersolution of (CN) or (DBC) in Ω if M1 ≥ max{|H(x,p)| : x∈ Ω,p∈ B(0,C)}. We recall (see [25, 9] for instance) that if x∈ ∂Ω, then D+uk −(x,t) = {(Duk 0(x)+λn˜(x),−M1) : λ≤ 0}, where D+uk −”
Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions (2017, unknown): “Lions [11].”