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Research Papers

Weighted Aleksandrov estimates: PDE and stochastic versions

N. V. Krylov

127 Vincent Hall, University of Minnesota, Minneapolis, MN, 55455

Abstract: Several pointwise estimates are proved for solutions of linear elliptic equations with measurable coefficients in smooth domains through the weighted $ L_d$-norm of the free term. The weights allow the free term to blow up near the boundary. Weighted estimates for occupation times of diffusion processes are also presented.

Keywords: weights, Aleksandrov estimates, elliptic equations.

MSC: 35J15, 35J60, 60H05

Received: 24.09.2018

Language: English

 English version: St. Petersburg Mathematical Journal, 2020, 31:3, 509–520

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