Maximal \(L_p\)\(L_q\) regularity for the quasi-steady elliptic problems

Abstract

In this paper, we consider maximal regularity for the vector-valued quasi-steady linear elliptic problems. The equations are the elliptic equation in the domain and the evolution equations on its boundary. We prove the maximal \(L_p\)\(L_q\) regularity for these problems and give examples that our results are applicable. The Lopatinskii–Shapiro and the asymptotic Lopatinskii–Shapiro conditions are important to get boundedness of solution operators.

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Acknowledgements

The first author was supported by the Program for Leading Graduate Schools, MEXT, Japan. Second author was supported by JSPS KAKENHI Grant No. 19K23408.

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Correspondence to Naoto Kajiwara.

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Furukawa, K., Kajiwara, N. Maximal \(L_p\)\(L_q\) regularity for the quasi-steady elliptic problems. J. Evol. Equ. (2020). https://doi.org/10.1007/s00028-020-00638-2

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Keywords

  • Maximal \(L_p\)\(L_q\) regularity
  • Quasi-steady problems