Geodesic
The convergence of nonnegative solutions for the family of problems − Δpu = λeu as p →∞
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 569-578 Cet article a éte moissonné depuis la source Numdam

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Let Ω ⊂ ℝ n , ( N ≥ 2 ) be a bounded domain with smooth boundary. We show the existence of a positive real number λ * such that for each λ ∈ ( 0 , λ * ) and each real number p > N the equation - Δ p u = λ e u in in Ω subject to the homogeneous Dirichlet boundary condition possesses a nonnegative solution u p . Next, we analyze the asymptotic behavior of u p as  p → ∞ and we show that it converges uniformly to the distance function to the boundary of the domain.

DOI : 10.1051/cocv/2017048
Classification : 35D30, 35D40, 35J60, 47J30, 46E30
Keywords: Weak solutionviscosity solution, nonlinear elliptic equations, asymptotic behavior, distance function to the boundary

Mihăilescu, Mihai 1 ; Stancu−Dumitru, Denisa 1 ; Varga, Csaba 1

1 
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     author = {Mih\u{a}ilescu, Mihai and Stancu\ensuremath{-}Dumitru, Denisa and Varga, Csaba},
     title = {The convergence of nonnegative solutions for the family of problems \ensuremath{-} {\ensuremath{\Delta}\protect\textsubscript{p}u} = \ensuremath{\lambda}e\protect\textsuperscript{u} as p {\textrightarrow}\ensuremath{\infty}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {569--578},
     year = {2018},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {2},
     doi = {10.1051/cocv/2017048},
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     mrnumber = {3816405},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017048/}
}
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Mihăilescu, Mihai; Stancu−Dumitru, Denisa; Varga, Csaba. The convergence of nonnegative solutions for the family of problems − Δpu = λeu as p →∞. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 569-578. doi: 10.1051/cocv/2017048

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