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Generalized perimeters and gradient estimates

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  • معلومة اضافية
    • Contributors:
      Institut de Mathématiques de Toulouse UMR5219 (IMT); Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J); Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3); Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)
    • بيانات النشر:
      CCSD
    • الموضوع:
      2025
    • Collection:
      Université Toulouse III - Paul Sabatier: HAL-UPS
    • نبذة مختصرة :
      We use a variational formulation to define a generalized notion of perimeter, from which we derive abstract isoperimetric Cheeger's inequalities via gradient estimates on solutions of Poisson equations. Our abstract framework unifies many existing results and in particular allows us to recover the $W_1-W^{1,1}$ transport inequality, which strengthens the usual transport-information inequality. Conversely, we also prove that Cheeger's inequality implies certain first order Calderón-Zygmund-type gradient estimates.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2411.05437; ARXIV: 2411.05437
    • الدخول الالكتروني :
      https://hal.science/hal-04772401
      https://hal.science/hal-04772401v3/document
      https://hal.science/hal-04772401v3/file/Generalized%20perimeters%20and%20gradient%20estimates.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.370B205E