On the contraction properties for weak solutions to linear elliptic equations with L²-drifts of negative divergence

2023/02/02 by Haesung Lee, Lee, Haesung · 1 citation
Computer Science · Engineering · Mathematics · #31C25 #35B35 (Secondary) #35J15 #35J25 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.01211

openalex publication_date 2023/02/02 · openalex created_date 2023/02/04 · openalex updated_date 2026/07/28

Abstract

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with L²-drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the L^r-contraction properties of the unique weak solutions. Indeed, using the Dirichlet form theory, we construct a sub-Markovian C₀-resolvent of contractions and identify it to the weak solutions. Furthermore, we derive an L¹-stability result through an extended version of the L¹-contraction property.

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• Notes on L²-estimates in linear elliptic equations with general coefficients

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