$Γ$-convergence of some super quadratic functionals with singular weights
| dc.creator | Palatucci, Giampiero | |
| dc.creator | Sire, Yannick | |
| dc.date | 2009-03-05 | |
| dc.date.accessioned | 2026-07-07T12:49:19Z | |
| dc.date.available | 2026-07-07T12:49:19Z | |
| dc.description | We study the $Γ$-convergence of the following functional ($p>2$) $$ F_ε(u):=ε^{p-2}\int_Ω|Du|^p d(x,\partial Ω)^{a}dx+\frac{1}{ε^{\frac{p-2}{p-1}}}\int_ΩW(u) d(x,\partial Ω)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrtε}\int_{\partialΩ}V(Tu)d\mathcal{H}^2, $$ where $Ω$ is an open bounded set of $\mathbb{R}^3$ and $W$ and $V$ are two non-negative continuous functions vanishing at $α, β$ and $α', β'$, respectively. In the previous functional, we fix $a=2-p$ and $u$ is a scalar density function, $Tu$ denotes its trace on $\partialΩ$, $d(x,\partial Ω)$ stands for the distance function to the boundary $\partial\Om$. We show that the singular limit of the energies $F_ε$ leads to a coupled problem of bulk and surface phase transitions. | |
| dc.identifier | https://arxiv.org/abs/0903.0984 | |
| dc.identifier | http://arxiv.org/abs/0903.0984 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222363 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 82B26, 49J45; 49Q20 | |
| dc.title | $Γ$-convergence of some super quadratic functionals with singular weights | |
| dc.type | text |