Let be a bounded domain with smooth boundary. We show the existence of a positive real number such that for each and each real number the equation in in subject to the homogeneous Dirichlet boundary condition possesses a nonnegative solution . Next, we analyze the asymptotic behavior of as and we show that it converges uniformly to the distance function to the boundary of the domain.
Mots-clés : Weak solutionviscosity solution, nonlinear elliptic equations, asymptotic behavior, distance function to the boundary
@article{COCV_2018__24_2_569_0,
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},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017048},
zbl = {1404.35311},
mrnumber = {3816405},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2017048/}
}
TY - JOUR AU - Mihăilescu, Mihai AU - Stancu−Dumitru, Denisa AU - Varga, Csaba TI - The convergence of nonnegative solutions for the family of problems − Δpu = λeu as p →∞ JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 569 EP - 578 VL - 24 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2017048/ DO - 10.1051/cocv/2017048 LA - en ID - COCV_2018__24_2_569_0 ER -
%0 Journal Article %A Mihăilescu, Mihai %A Stancu−Dumitru, Denisa %A Varga, Csaba %T The convergence of nonnegative solutions for the family of problems − Δpu = λeu as p →∞ %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 569-578 %V 24 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2017048/ %R 10.1051/cocv/2017048 %G en %F COCV_2018__24_2_569_0
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. http://www.numdam.org/articles/10.1051/cocv/2017048/
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