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Existence of a unique positive entropy solution to a singular fractional Laplacian

Bayrami Aminlouee, M ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/17476933.2020.1743984
  3. Publisher: Taylor and Francis Ltd , 2020
  4. Abstract:
  5. In this paper, we study the existence of a positive solution to the elliptic problem: (Formula presented.) Here (Formula presented.) (N>2s) is an open bounded domain with smooth boundary, (Formula presented.) and (Formula presented.). For (Formula presented.), we take advantage of the convexity of Ω. The operator (Formula presented.) indicates the restricted fractional Laplacian, and μ is a non-negative Radon measure as a source term. The assumptions on f and h will be precised later. Besides, we will discuss the notion of entropy solution and its uniqueness for some specific measures. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Fractional Laplacian ; Positive entropy solution ; Singular nonlinearity ; Uniqueness
  8. Source: Complex Variables and Elliptic Equations ; 2020
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/17476933.2020.1743984?journalCode=gcov20