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Properties of the free boundary near the fixed boundary of the double obstacle problems.
- Source :
- Bulletin of Mathematical Sciences (World Scientific); Dec2022, Vol. 12 Issue 3, p1-30, 30p
- Publication Year :
- 2022
-
Abstract
- In this paper, we study the tangential touch and C¹ regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a/2 x<subscript>n</subscript>² or a/2 x<subscript>n</subscript>² + bx<subscript>n</subscript>x<subscript>1</subscript> for some b ∈ ℝ, b ≠ 0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16643607
- Volume :
- 12
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Bulletin of Mathematical Sciences (World Scientific)
- Publication Type :
- Academic Journal
- Accession number :
- 162714315
- Full Text :
- https://doi.org/10.1142/S1664360721500090