We review upper and lower bound isoperimetric properties of the fundamental eigenfunction of the Dirichlet Laplacian and announce new reverse Holder type inequalities for norms of this function in the case of a wedgelike membrane.
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MAX-TO-MEAN RATIO ESTIMATES FOR THE FUNDAMENTAL EIGENFUNCTION OF THE DIRICHLET LAPLACIAN
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Najoua Gamara - Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia
Abdelhalim Hasnaoui - Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia