In this paper a rearrangement minimization problem corresponding to solutions of the p -Laplacian equation is considered. The solution of the minimization problem determines the optimal way of exerting external forces on a membrane in order to have a minimum displacement. Geometrical and topological properties of the optimizer is derived and the analytical solution of the problem is obtained for circular and annular membranes. Then, we find nearly optimal solutions which are shown to be good approximations to the minimizer for specific ranges of the parameter values in the optimization problem. A robust and efficient numerical algorithm is developed based upon rearrangement techniques to derive the solution of the minimization problem for domains with different geometries in ℝ 2 and ℝ 3 .
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This content will become publicly available on January 29, 2025
The asymptotic p-Poisson equation as $$p \rightarrow \infty $$ in Carnot-Carathéodory spaces
In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as $p\to \infty$ in Carnot-Carathéodory spaces. In particular, introducing a suitable notion of differentiability, extend the celebrated result of Bhattacharya et al. (Rend Sem Mat Univ Politec Torino Fascicolo Speciale 47:15–68, 1989) and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the infinity- Laplacian and the Eikonal equation.
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- Award ID(s):
- 2141297
- PAR ID:
- 10519865
- Publisher / Repository:
- Mathematische Annalen - Springer Verlag
- Date Published:
- Journal Name:
- Mathematische Annalen
- ISSN:
- 0025-5831
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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