Weak regularity of degenerate elliptic equations
- Authors: Gol’dshtein V.1, Ukhlov A.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 38, No 2 (2017)
- Pages: 262-270
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198951
- DOI: https://doi.org/10.1134/S1995080217020093
- ID: 198951
Cite item
Abstract
Let φ: Ω → D be a conformal mapping of a bounded simply connected planar domain Ω onto the unit disc D ⊂ ℝ2. We prove existence and uniqueness in Ω of weak solutions of a degenerate Poisson equation for a hyperbolic weight h(z) = |φz′|2 in a corresponding two weighted Sobolev space W21 (Ω, h, 1).Here φz′ is a complex derivative. We also study weak regularity of the solutions in conformal regular domains. The domain Ω is a conformal regular domain [4] if (φ−1)w′ ∈ Lα(D) for some α > 2.
Keywords
About the authors
V. Gol’dshtein
Department of Mathematics
Author for correspondence.
Email: vladimir@bgu.ac.il
Israel, Beer Sheva, 84105
A. Ukhlov
Department of Mathematics
Email: vladimir@bgu.ac.il
Israel, Beer Sheva, 84105