کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4604081 | 1337415 | 2016 | 19 صفحه PDF | دانلود رایگان |
• We show that W2,nW2,n solutions to our type of problems are C1,1C1,1.
• The free boundary is shown to be C1C1 under additional natural assumptions.
• The results above are extended to the parabolic setting.
We consider fully nonlinear obstacle-type problems of the form{F(D2u,x)=f(x)a.e. in B1∩Ω,|D2u|≤Ka.e. in B1\Ω, where Ω is an open set and K>0K>0. In particular, structural conditions on F are presented which ensure that W2,n(B1)W2,n(B1) solutions achieve the optimal C1,1(B1/2)C1,1(B1/2) regularity when f is Hölder continuous. Moreover, if f is positive on B‾1, Lipschitz continuous, and {u≠0}⊂Ω{u≠0}⊂Ω, we obtain interior C1C1 regularity of the free boundary under a uniform thickness assumption on {u=0}{u=0}. Lastly, we extend these results to the parabolic setting.
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 33, Issue 5, September–October 2016, Pages 1259–1277