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Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation

Author

Listed:
  • Antonino Morassi

    (Dipartimento di Georisorse e Territorio, Universita' degli Studi di Udine, via Cotonificio 114, 33100 Udine.)

  • Edi Rosset

    (Dipartimento di Matematica e Informatica, Universita' degli Studi di Trieste, via Valerio 12/1, 34127 Trieste.)

  • Sergio Vessella

    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

Abstract

We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation. Among these, we prove a stability estimate for the Cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate. The paper is self-contained and the Carleman estimate, from which the sharp three sphere inequality is derived, is proved in an elementary and direct way based on standard integration by parts.

Suggested Citation

  • Antonino Morassi & Edi Rosset & Sergio Vessella, 2010. "Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation," Working Papers - Mathematical Economics 2010-11, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:flo:wpaper:2010-11
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