Non-absolutely Convergent Generalized Laplacian

Author(s):  
Jan Malý ◽  
Ivan Netuka
Author(s):  
Vesa Mustonen ◽  
Matti Tienari

Let m: [ 0, ∞) → [ 0, ∞) be an increasing continuous function with m(t) = 0 if and only if t = 0, m(t) → ∞ as t → ∞ and Ω C ℝN a bounded domain. In this note we show that for every r > 0 there exists a function ur solving the minimization problemwhere Moreover, the function ur is a weak solution to the corresponding Euler–Lagrange equationfor some λ > 0. We emphasize that no Δ2-condition is needed for M or M; so the associated functionals are not continuously differentiable, in general.


2014 ◽  
Vol 44 (9) ◽  
pp. 1646-1660 ◽  
Author(s):  
Jesus Martinez-del-Rincon ◽  
Michal Lewandowski ◽  
Jean-Christophe Nebel ◽  
Dimitrios Makris

2020 ◽  
Vol 17 (4) ◽  
pp. 651-655 ◽  
Author(s):  
Tayeb Benzenati ◽  
Yousri Kessentini ◽  
Abdelaziz Kallel ◽  
Hind Hallabia

2020 ◽  
Vol 58 (9) ◽  
pp. 6152-6167 ◽  
Author(s):  
Gemine Vivone ◽  
Stefano Marano ◽  
Jocelyn Chanussot

Sign in / Sign up

Export Citation Format

Share Document