Vanishing viscosity for uniformly convex Hamilton-Jacobi equations converges at the optimal rate O(epsilon log epsilon), improving the old O(sqrt(epsilon)) bound.
Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
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abstract
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques \`a la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples.
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Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations
Vanishing viscosity for uniformly convex Hamilton-Jacobi equations converges at the optimal rate O(epsilon log epsilon), improving the old O(sqrt(epsilon)) bound.