کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773496 | 1413421 | 2017 | 24 صفحه PDF | دانلود رایگان |
This work is devoted to the study of nonvariational, singularly perturbed elliptic equations of degenerate type. The governing operator is anisotropic and ellipticity degenerates along the set of critical points. The singular behavior is of order O(1ϵ) along ϵ-level layers {uϵâ¼Ïµ}, and a non-homogeneous source acts in the noncoincidence region {uϵ>ϵ}. We obtain the precise geometric behavior of solutions near ϵ-level surfaces, by means of optimal regularity and sharp geometric nondegeneracy. We further investigate Hausdorff measure properties of ϵ-level surfaces. The analysis of the asymptotic limits as the ϵ parameter goes to zero is also carried out. The results obtained are new even if restricted to the uniformly elliptic, isotropic setting.
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 34, Issue 3, MayâJune 2017, Pages 655-678