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Regularity for systems

  • Luigi Ambrosio
  • Alessandro Carlotto
  • Annalisa Massaccesi
Chapter
Part of the Publications of the Scuola Normale Superiore book series (PSNS, volume 18)

Abstract

In the last section of the previous chapter we presented De Giorgi’s regularity result for solutions uH1 (Ω;ℝ) of the scalar elliptic problem
$$\sum\limits_{\alpha ,\beta } {{\partial _{{\chi _\alpha }}}({A^{\alpha \beta }}(x){\partial _{{\chi _\beta }}}u(x)) = 0} $$
with bounded Borel coefficients Aαß satisfying λI ≤ A ≤ ΛI: we proved that in fact \(u \in C_{{\text{loc}}}^{0,\upsilon }(\Omega ;\mathbb{R})\), with ϑ = ϑ(n, λ, Λ).

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Copyright information

© Scuola Normale Superiore Pisa 2018

Authors and Affiliations

  • Luigi Ambrosio
    • 1
  • Alessandro Carlotto
    • 2
  • Annalisa Massaccesi
    • 3
  1. 1.Scuola Normale SuperiorePisaItalia
  2. 2.ETHZürichSwitzerland
  3. 3.Università di VeronaVeronaItalia

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