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SUMMARY:Γ-Convergence of Higher Order Phase Transition Models. [Obersemin
 ar Analysis]
DTSTART:20260401T121500Z
DTEND:20260401T141500Z
DTSTAMP:20260716T200000Z
UID:indico-event-1193@math-events.uni-bonn.de
CONTACT:zemas@iam.uni-bonn.de
DESCRIPTION:Speakers: Gianna Götzmann (Uni Augsburg)\n\nWe investigate th
 e asymptotic behavior as $\\varepsilon \\to 0$ of singularly perturbed pha
 se transition models of order $n \\geq 2$\, given by$$G_\\varepsilon^{\\la
 mbda\,n}[u] :=\\int_I \\frac 1\\varepsilon W(u) -\\lambda\\varepsilon^{2n-
 3} (u^{(n-1)})^2 + \\varepsilon^{2n-1} (u^{(n)})^2 \\mathcal{d} x\, \\quad
  u \\in W^{n\,2}(I)\,$$where $\\lambda >0$ is fixed\, $I \\subset \\mathbb
 {R}$ is an open bounded interval\, and $W \\in C^0(\\mathbb{R})$ is a suit
 able double-well potential. We find that there exists a positive critical 
 parameter depending on $W$ and $n$\, such that the $\\Gamma$-limit of $G_\
 \varepsilon^{\\lambda\,n}$ with respect to the $L^1$-topology is given by 
 a sharp interface functional in the subcritical regime. The cornerstone fo
 r the corresponding compactness property is a novel nonlinear interpolatio
 n inequality involving higher-order derivatives\, which is based on Gaglia
 rdo-Nirenberg type inequalities.\n\nhttps://math-events.uni-bonn.de/event/
 1193/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1193/
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