Journals
Resources
About Us
Open Access
Go to previous page

Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators

Year:    2021

Author:    Yanyan Li, Zhuolun Yang

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 114–128

Abstract

We study the insulated conductivity problem with inclusions embedded in a bounded domain in Rn. When the distance of inclusions, denoted by ε, goes to 0, the gradient of solutions may blow up. When two inclusions are strictly convex, it was known that an upper bound of the blow-up rate is of order ε1/2 for n=2, and is of order ε1/2+β for some β>0 when dimension n3. In this paper, we generalize the above results for insulators with flatter boundaries near touching points.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2021.pr80.12

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 114–128

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Conductivity problem harmonic functions maximum principle gradient estimates.

Author Details

Yanyan Li Email

Zhuolun Yang Email

  1. Optimal estimates for transmission problems including relative conductivities with different signs

    Dong, Hongjie | Yang, Zhuolun

    Advances in Mathematics, Vol. 428 (2023), Iss. P.109160

    https://doi.org/10.1016/j.aim.2023.109160 [Citations: 3]
  2. Gradient estimates for the insulated conductivity problem: The case of m-convex inclusions

    Zhao, Zhiwen

    Journal of Mathematical Physics, Vol. 64 (2023), Iss. 3

    https://doi.org/10.1063/5.0100907 [Citations: 1]
  3. Gradient estimates for the insulated conductivity problem with inclusions of the general m‐convex shapes

    Zhao, Zhiwen

    ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 103 (2023), Iss. 12

    https://doi.org/10.1002/zamm.202200324 [Citations: 0]
  4. Gradient estimates for the insulated conductivity problem: The non-umbilical case

    Dong, Hongjie | Li, YanYan | Yang, Zhuolun

    Journal de Mathématiques Pures et Appliquées, Vol. 189 (2024), Iss. P.103587

    https://doi.org/10.1016/j.matpur.2024.06.002 [Citations: 2]
  5. Gradient estimates of solutions to the insulated conductivity problem in dimension greater than two

    Li, YanYan | Yang, Zhuolun

    Mathematische Annalen, Vol. 385 (2023), Iss. 3-4 P.1775

    https://doi.org/10.1007/s00208-022-02368-x [Citations: 12]
  6. The Insulated Conductivity Problem with p-Laplacian

    Dong, Hongjie | Yang, Zhuolun | Zhu, Hanye

    Archive for Rational Mechanics and Analysis, Vol. 247 (2023), Iss. 5

    https://doi.org/10.1007/s00205-023-01926-0 [Citations: 1]
  7. Optimal estimates for the conductivity problem close to the boundary in dimension greater than two

    Ma, Linjie

    Discrete and Continuous Dynamical Systems, Vol. 43 (2023), Iss. 1 P.162

    https://doi.org/10.3934/dcds.2022144 [Citations: 0]