On the kinetic Fokker-Planck equation in the half-space with absorbing barriers
Hyung HwangJuhi JangJaewoo Jung
35Q8435G1635H10Fokker-PlanckIntial-boundary value problemHypoellipticityExponential decay
We establish a well-posedness theory of classical solutions of the Fokker-Planck equation---the forward Kolmogorov equation in the half-space $\mathbb{R}^3_{+}$ with absorbing boundary conditions. We first build a theory for the regularized equations near the singular set by the method of characteristics, and then pass to the limit by uniform $L^1$ and $L^{\infty}$ estimates. We prove the hypoellipticity up to the boundary away from the singular set, and moreover, we show that the solutions are H\"older continuous up to the singular set.
Indiana University Mathematics Journal
2015
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10.1512/iumj.2015.64.5679
10.1512/iumj.2015.64.5679
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Indiana Univ. Math. J. 64 (2015) 1767 - 1804
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