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A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities

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  • معلومة اضافية
    • Contributors:
      Universidade Aberta [Lisboa]; Grupo de Física Matemática - Group of Mathematical Physics (GFM); Universidade de Lisboa = University of Lisbon (ULISBOA); Pontificia Universidad Católica de Chile (UC); Department of Theoretical Physics, Nuclear Physics Institute; Czech Academy of Sciences [Prague] (CAS); Institut de Mathématiques de Marseille (I2M); Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS); Universidade de Lisboa (ULISBOA); Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
    • بيانات النشر:
      Springer Science and Business Media LLC, 2021.
    • الموضوع:
      2021
    • نبذة مختصرة :
      We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.
      Comment: 34 pages, 4 figures
    • ISSN:
      1432-0916
      0010-3616
    • الرقم المعرف:
      10.1007/s00220-021-03959-6
    • الرقم المعرف:
      10.1007/s00220-021-03959-6⟩
    • Rights:
      OPEN
    • الرقم المعرف:
      edsair.doi.dedup.....2b5278c5d79433fd72d7908d9b02d0fb