BOUNDS FOR THE FIRST DIRICHLET EIGENVALUE OF TRIANGLES AND QUADRILATERALS

作者：Freitas Pedro^*; Siudeja Batlomiej

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2010, 16(3): 648-676.

DOI：10.1051/cocv/2009018

• Dirichlet eigenvalues
• polygons
• variational bounds

We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Polya and Szego's [Annals of Mathematical Studies 27 (1951)] lower bound for quadrilaterals and extend Hersch's [Z. Angew. Math. Phys. 17 (1966) 457-460] upper bound for parallelograms to general quadrilaterals.

• 出版日期2010-9