Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
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 and homogenization 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.
discuss several consequences, ranging from $ L^ p $-rates of convergence for the vanishing
viscosity approximation and homogenization 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.
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from -rates of convergence for the vanishing viscosity approximation and homogenization 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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