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Ravisankar, Sivaguru (2012)
Languages: English
Types: Preprint
Subjects: 35B65, Mathematics - Classical Analysis and ODEs, Mathematics - Analysis of PDEs
Let \Omega\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We show that a harmonic function in \Omega that is Lipschitz along a family of curves transversal to b\Omega is Lipschitz in \Omega. The space of Lipschitz functions we consider is defined using the notion of a majorant which is a certain generalization of the power functions t^\alpha, 0<\alpha<1.
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    • [7] Miroslav Pavlovic´. Lipschitz conditions on the modulus of a harmonic function. Rev. Mat. Iberoam., 23(3):831-845, 2007.
    • [8] Sivaguru Ravisankar. Lipschitz properties of harmonic and holomorphic functions. Ph.D. diss., The Ohio State University, 2011.
    • [9] A. Zygmund. Trigonometric series. 2nd ed. Vols. I, II. Cambridge University Press, New York, 1959.
    • DEPARTMENT OF MATHEMATICS, THE OHIO STATE UNIVERSITY, COLUMBUS, OHIO 43210 E-mail address:
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