Existence of positive solutions for a singular elliptic problem with\n critical exponent and measure data

2020/02/26 by Akasmika Panda, Debajyoti Choudhuri, Panda, Akasmika +3
Computer Science · Mathematics · #35A15 #35J60 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2002.11393

openalex publication_date 2020/02/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a positive it SOLA (Solutions Obtained as Limits\nof Approximations) to the following PDE involving fractional power of\nLaplacian n
beginsplit\n (-
Delta)^suamp;=
frac1u^
gamma+
lambda u^{2_s^*-1}+
mu ~
textin~
Omega,\nuamp;gt;0~
textin~
Omega, uamp;= 0~
textin~
mathbbR^N
setminus
Omega.\n
endsplit\n Here, \Ω is a bounded domain of \ℝ^N, s\∈\n(0,1), 2s<N, \λ,\γ\∈ (0,1), 2_s^*=\(2N)/(N-2s) is the\nfractional critical Sobolev exponent and \μ is a nonnegative bounded Radon\nmeasure in \Ω.\n

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