Year: 2025
Type: article
Abstract: Let $$\mu $$ μ be a positive measure supported on a planar domain $$\Omega $$ Ω . We consider the behavior of the balayage measure $$\nu :=\textrm{Bal}(\mu ,\partial \Omega )$$ ν : = Bal ( μ , ∂ Ω ) near a point $$z_{0}\in \partial \Omega $$ z 0 ∈ ∂ Ω at which $$\Omega $$ Ω has an outward-pointing cusp. Assuming that the order and coefficient of tangency of the cusp are $$d>0$$ d > 0 and $$a>0$$ a > 0 , respectively, and that $$d\mu (z) \asymp |z-z_{0}|^{2b-2}d^{2}z$$ d μ ( z ) ≍ | z - z 0 | 2 b - 2 d 2 z as $$z\rightarrow z_0$$ z → z 0 for some $$b > 0$$ b > 0 (here $$d^2z$$ d 2 z is the Lebesgue measure on $$\mathbb {C}$$ C ), we obtain the leading order term of $$\nu $$ ν near $$z_{0}$$ z 0 . This leading
Source: Potential Analysis
Authors: Christophe Charlier, Jonatan Lenells
Institutions: Lund University, KTH Royal Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funders: Lunds Universitet, Vetenskapsrådet
OpenAlex ID: W4409136769