Regularization by 1/2-Laplacian and vanishing viscosity approximation of HJB equations

Imran H. Biswas

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arXiv · 1205.6943

Regularization by 1/2-Laplacian and vanishing viscosity approximation of HJB equations

Imran H. Biswas

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Abstract

We investigate the regularizing effect of adding small fractional Laplacian, with critical fractional exponent 1/2, 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 1/2-Laplacian and derive an explicit rate convergence for the vanishing viscosity limit.

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Imran H. Biswas. 2012-05-31. Regularization by 1/2-Laplacian and vanishing viscosity approximation of HJB equations. https://arxiv.org/abs/1205.6943

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