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The Surface Diffusion Flow with Elasticity in the Plane

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Abstract

In this paper we prove short-time existence of a smooth solution in the plane to the surface diffusion equation with an elastic term and without an additional curvature regularization. We also prove the asymptotic stability of strictly stable stationary sets.

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Acknowledgements

The work of Nicola Fusco was supported by PRIN MIUR project 2015PA5MP7 ‘Calcolo delle Variazioni’. Nicola Fusco and Massimiliano Morini are members of the GNAMPA-INDAM.

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Authors and Affiliations

  1. Università degli Studi di Napoli Federico II, Napoli, Italy

    Nicola Fusco

  2. Jyväskylän Yliopisto, Matematiikan ja Tilastotieteen Laitos, Jyväskylä, Finland

    Vesa Julin

  3. Università degli Studi di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Parma, Italy

    Massimiliano Morini

Authors
  1. Nicola Fusco
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  2. Vesa Julin
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  3. Massimiliano Morini
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Correspondence to Nicola Fusco.

Additional information

Communicated by L. Caffarelli

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Fusco, N., Julin, V. & Morini, M. The Surface Diffusion Flow with Elasticity in the Plane. Commun. Math. Phys. 362, 571–607 (2018). https://doi.org/10.1007/s00220-018-3200-2

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  • DOI: https://doi.org/10.1007/s00220-018-3200-2

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