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The Hadamard variational formula and the Minkowski problem for p-Capacity
U.Dini, Firenze, Italy.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
U.Dini, Firenze, Italy.
Memorial University of Newfoundland, St. John's, Canada.
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2015 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 285, 1511-1585 p.Article in journal (Refereed) Published
Abstract [en]

A Hadamard variational formula for p-capacity of convex bodies in R-n is established when 1 < p < n. The formula is applied to solve the Minkowski problem for p-capacity which involves a degenerate Monge Ampere type equation. zkiniqueness for the Minkowski problem for p-capacity is established when 1 < p < n and existence and regularity when 1 < p < 2. These results are (non-linear) extensions of the now classical solution of Jerison of the Minkowski problem for electrostatic capacity (p = 2).

Place, publisher, year, edition, pages
2015. Vol. 285, 1511-1585 p.
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URN: urn:nbn:se:uu:diva-214109DOI: 10.1016/j.aim.2015.06.022ISI: 000376417800041OAI: diva2:684080
Available from: 2014-01-07 Created: 2014-01-07 Last updated: 2016-07-07Bibliographically approved

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