Regularization by -Laplacian and vanishing viscosity approximation of HJB equations
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文摘
We investigate the regularizing effect of adding small fractional Laplacian, with critical fractional exponent , to a general first order HJB equation. Our results include some regularity estimates for the viscosity solutions of such perturbations, making the solutions classically well-defined. Most importantly, we use these regularity estimates to study the vanishing viscosity approximation to first order HJB equations by -Laplacian and derive an explicit rate convergence for the vanishing viscosity limit.