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Mathematics > Analysis of PDEs

arXiv:1804.08398 (math)
[Submitted on 23 Apr 2018 (v1), last revised 11 May 2018 (this version, v2)]

Title:The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach

Authors:Jesús Ildefonso Díaz, David Gómez-Castro, Juan Luis Vázquez
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Abstract:We study the Dirichlet problem for the stationary Schrödinger fractional Laplacian equation $(-\Delta)^s u + V u = f$ posed in bounded domain $ \Omega \subset \mathbb R^n$ with zero outside conditions. We consider general nonnegative potentials $V\in L^1_{loc}(\Omega)$ and prove well-posedness of very weak solutions when the data are chosen in an optimal class of weighted integrable functions $f$. Important properties of the solutions, such as its boundary behaviour, are derived. The case of super singular potentials that blow up near the boundary is given special consideration. Related literature is commented.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35J10, 35D30, 35J67, 35J75
Cite as: arXiv:1804.08398 [math.AP]
  (or arXiv:1804.08398v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.08398
Related DOI: https://doi.org/10.1016/j.na.2018.05.001

Submission history

From: David Gómez-Castro [view email]
[v1] Mon, 23 Apr 2018 13:30:56 UTC (37 KB)
[v2] Fri, 11 May 2018 09:53:02 UTC (39 KB)
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