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Examples of twice differentiable functions with continuous Laplacian and unbounded Hessian

  • Pan, Yifei [1] ; Yan, Yu [2]
    1. [1] Purdue University

      Purdue University

      Township of Wabash, Estados Unidos

    2. [2] Biola University

      Biola University

      Estados Unidos

  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 2, 2024, págs. 453-479
  • Idioma: inglés
  • DOI: 10.1007/s13348-023-00395-8
  • Enlaces
  • Resumen
    • We construct examples of twice differentiable functions in with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.

  • Referencias bibliográficas
    • Coffman, A., Pan, Y.: Smooth counterexamples to strong unique continuation for a Beltrami system in C2 . Commun. Partial Differ. Equ. 37(12),...
    • Coffman, A., Pan, Y., Zhang, Y.: Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates....
    • Fernandez-Real, X., Ros-Oton, X.: Regularity Theory for Elliptic PDE. Zurich Lectures in Advanced Mathematics. European Mathematical Society,...
    • Ros-Oton, X.: Personal Communication
    • Wang, X.-J.: Schauder estimates for elliptic and parabolic equations. Chin. Ann. Math. Ser. B 27(6), 637–642 (2006)

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