The Hadamard variational formula and the Minkowski problem for p-capacity

A. Colesanti, K. Nyström, P. Salani, J. Xiao, D. Yang, G. Zhang

Research output: Contribution to journalArticle

Abstract

A Hadamard variational formula for p-capacity of convex bodies in Rn is established when 1 < p< n. The formula is applied to solve the Minkowski problem for p-capacity which involves a degenerate Monge-Ampère type equation. Uniqueness 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).

Original languageEnglish (US)
Article number5138
Pages (from-to)1511-1588
Number of pages78
JournalAdvances in Mathematics
Volume285
DOIs
StatePublished - Nov 5 2015

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Convex Body
Classical Solution
Electrostatics
Uniqueness
Regularity

Keywords

  • Convex domain
  • Existence
  • Minkowski inequality
  • Minkowski problem
  • Monge-Ampére equation
  • P-capacitary measure
  • P-capacity
  • P-equilibrium potential
  • P-Laplacian
  • Regularity
  • Uniqueness
  • Variational formula

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Hadamard variational formula and the Minkowski problem for p-capacity. / Colesanti, A.; Nyström, K.; Salani, P.; Xiao, J.; Yang, D.; Zhang, G.

In: Advances in Mathematics, Vol. 285, 5138, 05.11.2015, p. 1511-1588.

Research output: Contribution to journalArticle

Colesanti, A. ; Nyström, K. ; Salani, P. ; Xiao, J. ; Yang, D. ; Zhang, G. / The Hadamard variational formula and the Minkowski problem for p-capacity. In: Advances in Mathematics. 2015 ; Vol. 285. pp. 1511-1588.
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