On C1 -approximability of functions by solutions of second order elliptic equations on plane compact sets and C-analytic capacity

P. V. Paramonov, X. Tolsa

Research output: Contribution to journalArticleResearch

Abstract

© 2018, Springer Nature Switzerland AG. Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney C1-spaces on compact sets in R2 are obtained in terms of the respective C1-capacities. It is proved that the mentioned C1-capacities are comparable to the classic C-analytic capacity, and so have a proper geometric measure characterization.
Original languageEnglish
Pages (from-to)1133-1161
JournalAnalysis and Mathematical Physics
Volume9
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • C-analytic capacity
  • C -approximation 1
  • Curvature of measure
  • L-oscillation
  • LC -capacity 1
  • Localization operator of Vitushkin type
  • Second order homogeneous elliptic operator

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