Extremal energies of Laplacian operator: Different configurations for steady vortices

Mohammadi, Seyyed Abbas

doi:10.1016/j.jmaa.2016.09.011

Cited by 7 publications

(2 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based upon rearrangement techniques, we will find sequence of functions {f i } ∞ 0 ∈ N where the corresponding energies {F(f i )} ∞ 0 is decreasing. The numerical algorithm is a modification of the methods developed in [27,28,42]. The following theorem provides the main tool for generating the minimizing sequence.…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…Let α = 0, the optimal set D is a region in the body that should be heated to minimize F(D) which in this case, up to a normalization constant, the amount of heat presented in the region occupied by D [17,47]. It is noteworthy that Equation (1) and the corresponding optimization problem (3) can be interpreted differently, for instance see [27,42].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A rearrangement minimization problem corresponding top-Laplacian equation

Kao

Mohammadi

2022

ESAIM: COCV

Self Cite

View full text Add to dashboard Cite

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 $\mathbb{R}^2$ and $\mathbb{R}^3$.

show abstract

Section: Numerical Algorithmmentioning

confidence: 99%