scholarly journals Strong solutions to a fourth order exponential PDE describing epitaxial growth

2022 ◽  
Vol 306 ◽  
pp. 220-250
Author(s):  
Brock C. Price ◽  
Xiangsheng Xu
Keyword(s):  
Epitaxial Growth ◽  
Fourth Order ◽  
Strong Solutions

Beyond the Mountain Pass: Some Applications

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Ireneo Peral
Keyword(s):  
Epitaxial Growth ◽  
Nonlinear Problem ◽  
Fourth Order ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
The Common ◽  
Zhang Model ◽  
Supercritical Problem

AbstractWe will survey three applications of the famous Mountain Pass Lemma by Antonio Ambrosetti and Paul H. Rabinowitz, [6]. Precisely, we will present some results on the following problems:A model of growth and roughening of surfaces, usually called Kardar-Parisi-Zhang model.A supercritical problem involving Hardy-Leray potential with the pole at the boundary.A fourth order nonlinear problem related to epitaxial growth.The common characteristic of all these problems is that we have some extra difficulties in order to apply the Mountain Pass Lemma.

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