Regularity properties of viscosity solution of nonconvex Hamilton–Jacobi equations. Issue 6 (26th April 2019)

• Record Type: Journal Article
• Authors: Hoang, Nguyen
• Is Part Of: Applicable analysis. Volume 98:Issue 6(2019)
• Page Start: 1104
• Page End: 1119
• Publication Date: 2019-04-26
• Subjects: Hamilton–Jacobi equation -- regularity -- Hopf formula -- viscosity solution; 35D40 -- 35F21 -- 35F25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1416101
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: Some properties of characteristic curves in connection with the viscosity solution of the Hamilton–Jacobi equation( H, σ ) defined by the Hopf formulau ( t, x ) = max q ∈ R n { ⟨ x, q ⟩ - σ ∗ ( q ) - t H ( q ) } are studied. We are concerned with the points at which the solution u ( t, x ) is differentiable, and the strip of the formR = ( 0, θ ) × R n in the domainΩ where u ( t, x ) is of classC 1 ( R ) .