Regularity of the free boundary in the biharmonic obstacle problem
نویسندگان
چکیده
منابع مشابه
Regularity of the free boundary in the biharmonic obstacle problem
In this article we use flatness improvement argument to study the regularity of the free boundary for the biharmonic obstacle problem with zero obstacle. Assuming that the solution is almost one-dimensional, and that the non-coincidence set is an non-tangentially accessible (NTA) domain, we derive the C-regularity of the free boundary in a small ball centered at the origin. From the C-regularit...
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In this paper, we study the obstacle problem with obstacles whose Laplacians are not necessarily Hölder continuous. We show that the free boundary at a regular point is C if the Laplacian of the obstacle is negative and Dini continuous. We also show that this condition is sharp by giving a method to construct a counter-example when we weaken the requirement on the Laplacian of the obstacle by a...
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We study the regularity of the free boundary in the obstacle for the p-Laplacian, min { −∆pu, u − φ } = 0 in Ω ⊂ R. Here, ∆pu = div ( |∇u|p−2∇u ) , and p ∈ (1, 2) ∪ (2,∞). Near those free boundary points where ∇φ 6= 0, the operator ∆p is uniformly elliptic and smooth, and hence the free boundary is well understood. However, when ∇φ = 0 then ∆p is singular or degenerate, and nothing was known ab...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2019
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-019-1638-5