Studies of efficient data structures to tackle the U-curve optimization problem
Regularity theory for classes of local and non-local degenerate elliptic equation
Solving nonconvex formulations of Euclidean steiner tree problems in N-space
| Full text | |
| Author(s): |
Santos, Jefferson Abrantes
;
Soares, Sergio H. Monari
Total Authors: 2
|
| Document type: | Journal article |
| Source: | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 59, n. 6, p. 23-pg., 2020-10-08. |
| Abstract | |
An optimization problem with volume constraint involving the Phi-Laplacian in Orlicz-Sobolev spaces is considered for the case where Phi does not satisfy the natural condition introduced by Lieberman. A minimizer u(Phi) having non-degeneracy at the free boundary is proved to exist and some important consequences are established like the Lipschitz regularity of uF along the free boundary, that the set {u(Phi) > 0} has uniform positive density, that the free boundary is porous with porosity delta > 0 and has finite (N - delta)-Hausdorff measure. Under a geometric compatibility condition set up by Rossi and Teixeira, it is established the behavior of a l-quasilinear optimal design problem with volume constraint for l small. As l -> 0(+), we obtain a limiting free boundary problem driven by the infinity-Laplacian operator and find the optimal shape for the limiting problem. The proof is based on a penalization technique and a truncated minimization problem in terms of the Taylor polynomial of Phi. (AU) | |
| FAPESP's process: | 18/11664-0 - Quasilinear problems in Orlicz-Sobolev spaces |
| Grantee: | Sergio Henrique Monari Soares |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |
| FAPESP's process: | 16/16745-3 - Limiting free boundary problem in Orlicz-Sobolev spaces |
| Grantee: | Sergio Henrique Monari Soares |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |