De Giorgi Techniques Applied to Hamilton-Jacobi Equations with Unbounded Right-Hand Side

2017/03/03 by Stokols, L. F., Vasseur, Alexis F.
#35B65 #35G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.01278

Abstract

In this article we obtain Holder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffusion and the smoothness of the Hamiltonian. Our work is in the spirit of a result by P. Cardaliaguet and L. Silvestre [5]. We utilize De Giorgi's method, which was introduced to this class of equations in [6].

Related

• Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side
• A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
• On the improvement of Hölder seminorms in superquadratic Hamilton-Jacobi equations
• De Giorgi Techniques Applied to The Holder Regularity of Solutions to Hamilton-Jacobi Equations
• Existence and global Lipschitz estimates for unbounded classical solutions of a Hamilton-Jacobi equation