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Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data

Volume 258 / 2021

Tomasz Klimsiak Studia Mathematica 258 (2021), 121-156 MSC: Primary 35J87, 35J57; Secondary 47G20. DOI: 10.4064/sm190716-11-5 Published online: 13 November 2020


We consider the obstacle problem with irregular barriers for semilinear elliptic equations involving measure data and an operator corresponding to a general quasi-regular Dirichlet form. We prove existence and uniqueness of a solution as well as its representation as an envelope of supersolutions to some related partial differential equation. We also prove regularity results for the solution and the Lewy–Stampacchia inequality.


  • Tomasz KlimsiakFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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