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Ellipticity on spaces with higher singularities

Abstract

We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.

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Acknowledgements

The work was supported by a National Science Foundation of USA (Grant No. DMS-1408839) and a McDevitt Endowment Fund at Georgetown University. The paper is based on lectures which were given by the authors at City University of Hong Kong and Hong Kong Baptist University. The authors express their profound gratitude to Professor Tong Yang, Professor Tao Luo and Professor Yutian Li for their invitation and for the warm hospitality extended to them during their stay in Hong Kong. The authors also thank the Editorial Board for the invitation to contribute this paper to a special issue of Science China Mathematics in memory of Professor Minde Cheng at the centenary of his birth.

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Correspondence to Der-Chen Chang.

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Dedicated to the memory of Professor CHENG MinDe on the occasion of the centenary of his birth

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Chang, DC., Schulze, BW. Ellipticity on spaces with higher singularities. Sci. China Math. 60, 2053–2076 (2017). https://doi.org/10.1007/s11425-016-0519-9

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  • DOI: https://doi.org/10.1007/s11425-016-0519-9

Keywords

  • pseudo-differential operators
  • operator-valued symbols
  • Fourier and Mellin transforms

MSC(2010)

  • 35S35
  • 35J70