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2012•Complex Variables and Elliptic EquationsOpen access

Transversally Lipschitz harmonic functions are Lipschitz

Sivaguru Ravisankar

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Abstract

Let Ω ⊂ ℝ n be a bounded domain with C ∞ boundary. We show that a harmonic function in Ω that is Lipschitz along a family of curves transversal to bΩ is Lipschitz in Ω. The space of Lipschitz functions which we consider is defined using the notion of a majorant which is a certain generalization of the power functions t α, 0 < α < 1

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Let Ω ⊂ ℝ n be a bounded domain with C ∞ boundary. We show that a harmonic function in Ω that is Lipschitz along a family of curves transversal to bΩ is Lipschitz in Ω. The space of Lipschitz functions which we consider is defined using the notion of a majorant which is a certain generalization of the power functions t α, 0 < α < 1

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Available abstract

Let Ω ⊂ ℝ n be a bounded domain with C ∞ boundary. We show that a harmonic function in Ω that is Lipschitz along a family of curves transversal to bΩ is Lipschitz in Ω. The space of Lipschitz functions which we consider is defined using the notion of a majorant which is a certain generalization of the power functions t α, 0 < α < 1

Key concepts: Lipschitz continuity, Lipschitz domain, Mathematics, Omega, Bounded function, Harmonic function, Boundary (topology), Domain (mathematical analysis)

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