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- W3184227926 abstract "Abstract Let Ω be a bounded domain in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> {mathbb{R}^{n}} . Under appropriate conditions on Ω, we prove existence and uniqueness of continuous functions solving the Dirichlet problem associated to certain nonlinear mean value properties in Ω with respect to balls of variable radius. We also show that, when properly normalized, such functions converge to the p -harmonic solution of the Dirichlet problem in Ω for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>p</m:mi> <m:mo>⩾</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {pgeqslant 2} . Existence is obtained via iteration, a fundamental tool being the construction of explicit universal barriers in Ω." @default.
- W3184227926 created "2021-08-02" @default.
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- W3184227926 date "2021-04-30" @default.
- W3184227926 modified "2023-10-03" @default.
- W3184227926 title "<i>p</i>-harmonic functions by way of intrinsic mean value properties" @default.
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- W3184227926 doi "https://doi.org/10.1515/acv-2020-0101" @default.
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