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- W2095024899 abstract "For p -harmonic functions on unweighted R 2 , with 1 < p < ∞ , we show that if the boundary values f has a jump at an (asymptotic) corner point z 0 , then the Perron solution Pf is asymptotically a + b arg ( z − z 0 ) + o ( | z − z 0 | ) . We use this to obtain a positive answer to Baernstein's 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 ¯ . We also obtain various invariance results for functions with jumps and perturbations on small sets. For p > 2 these results are new also for continuous functions. Finally we look at generalizations to R n and metric spaces." @default.
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- W2095024899 date "2010-07-01" @default.
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- W2095024899 title "p-Harmonic functions with boundary data having jump discontinuities and Baernstein's problem" @default.
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- W2095024899 doi "https://doi.org/10.1016/j.jde.2010.03.002" @default.
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