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p-Harmonic functions with boundary data having jump discontinuities and Baernsteins problem
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
2010 (English)In: JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, Vol. 249, no 1, 1-36 p.Article in journal (Refereed) Published
Abstract [en]

For p-harmonic functions on unweighted R-2, with 1 andlt; p andlt; infinity, we show that if the boundary values f has a jump at an (asymptotic) corner point zo, then the Perron solution Pf is asymptotically a + b arg(z - z(0)) + o(vertical bar z z(0)vertical bar). We use this to obtain a positive answer to Baernsteins problem on the equality of the p-harmonic measure of a union G of open arcs on the boundary of the unit disc, and the p. harmonic measure of (G) over bar. We also obtain various invariance results for functions with jumps and perturbations on small sets. For p andgt; 2 these results are new also for continuous functions. Finally we look at generalizations to R-n and metric spaces.

Place, publisher, year, edition, pages
Elsevier Science B.V., Amsterdam , 2010. Vol. 249, no 1, 1-36 p.
Keyword [en]
Baernsteins problem, Boundary regularity, Dirichlet problem, Invariance, Jump discontinuity, Metric space, Nonlinear, Perron solution, Perturbation, Quasiminimizer, p-Harmonic, Potential theory, Resolutive, Semicontinuous
National Category
Social Sciences
URN: urn:nbn:se:liu:diva-57403DOI: 10.1016/j.jde.2010.03.002ISI: 000278406600001OAI: diva2:325537
Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2013-12-17

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Björn, Anders
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Applied MathematicsThe Institute of Technology
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