Results 91 to 100 of about 101,180 (174)
Sobolev inequalities for Neumann Laplacians on half spaces [PDF]
arXiv, 2017 We consider different fractional Neumann Laplacians of order s, 0
arxiv
Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group. [PDF]
Heliyon, 2022 Tsegaw BB.
europepmc +1 more source
Maximum principles for Laplacian and fractional Laplacian with critical integrability [PDF]
arXiv, 2019 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider the critical cases for Laplacian with zero order term and first order term. It is well known that for the Laplacian with zero order term $-\Delta +c(x)$ in $B_1$, $c(x)\in L^p(B_1)$($B_1\subset \mathbf{R}^n$), the critical ...
arxiv
Radial symmetry results for fractional Laplacian systems [PDF]
Nonlinear Analysis: Theory, Methods & Applications Volume 146,
November 2016, 2016 In this paper, we generalize the direct method of moving planes for the fractional Laplacian to the system case. Considering a coupled nonlinear system with fractional Laplacian, we first establish a decay at infinity principle and a narrow region principle. Using these principles, we obtain two radial symmetry results for the decaying solutions of the
arxiv
What Is the Fractional Laplacian?
, 2018 The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for ...
Lischke, Anna +10 more
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Carleman inequalities for fractional Laplacians and unique continuation [PDF]
arXiv, 2014 We obtain a unique continuation result for fractional Schr\"odinger operators with potential in Morrey spaces. This is based on Carleman inequalities for fractional Laplacians.
arxiv
Optimal partition problems for the fractional Laplacian [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2017 In this work, we prove an existence result for an optimal partition problem of the form $$\min \{F_s(A_1,\dots,A_m)\colon A_i \in \mathcal{A}_s, \, A_i\cap A_j =\emptyset \mbox{ for } i\neq j\},$$ where $F_s$ is a cost functional with suitable assumptions of monotonicity and lowersemicontinuity, $\mathcal{A}_s$ is the class of admissible domains and ...
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A new definition of the fractional Laplacian [PDF]
arXiv, 2002 It is noted that the standard definition of the fractional Laplacian leads to a hyper-singular convolution integral and is also obscure about how to implement the boundary conditions. This purpose of this note is to introduce a new definition of the fractional Laplacian to overcome these major drawbacks.
arxiv
Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians
, 2020 In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal ...
Wang, Pengyan, Chen, Wenxiong
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On fractional Laplacians [PDF]
arXiv, 2013 We compare two natural types of fractional Laplacians $(-\Delta)^s$, "Navier" and "Dirichlet" ones. We show that for $0
arxiv