TY - JOUR

T1 - Rearrangements and minimization of the principal eigenvalue of a nonlinear Steklov problem

AU - Emamizadeh, Behrouz

AU - Zivari-Rezapour, Mohsen

PY - 2011/11

Y1 - 2011/11

N2 - This paper, motivated by Del Pezzo et al. (2006) [1], discusses the minimization of the principal eigenvalue of a nonlinear boundary value problem. In the literature, this type of problem is called Steklov eigenvalue problem. The minimization is implemented with respect to a weight function. The admissible set is a class of rearrangements generated by a bounded function. We merely assume the generator is non-negative in contrast to [1], where the authors consider weights which are positively away from zero, in addition to being two-valued. Under this generality, more physical situations can be modeled. Finally, using rearrangement theory developed by Geoffrey Burton, we are able to prove uniqueness of the optimal solution when the domain of interest is a ball.

AB - This paper, motivated by Del Pezzo et al. (2006) [1], discusses the minimization of the principal eigenvalue of a nonlinear boundary value problem. In the literature, this type of problem is called Steklov eigenvalue problem. The minimization is implemented with respect to a weight function. The admissible set is a class of rearrangements generated by a bounded function. We merely assume the generator is non-negative in contrast to [1], where the authors consider weights which are positively away from zero, in addition to being two-valued. Under this generality, more physical situations can be modeled. Finally, using rearrangement theory developed by Geoffrey Burton, we are able to prove uniqueness of the optimal solution when the domain of interest is a ball.

KW - Existence

KW - Minimization

KW - Principal eigenvalue

KW - Rearrangement theory

KW - Steklov eigenvalue problem

KW - Uniqueness

UR - http://www.scopus.com/inward/record.url?scp=79959767760&partnerID=8YFLogxK

U2 - 10.1016/j.na.2011.05.056

DO - 10.1016/j.na.2011.05.056

M3 - Article

AN - SCOPUS:79959767760

SN - 0362-546X

VL - 74

SP - 5697

EP - 5704

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 16

ER -