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In this paper we will discuss three different problems which share the same conclusions. In the first one we revisit the well known Faber–Krahn inequality for the principal eigenvalue of the p-Laplace operator with zero homogeneous Dirichlet boundary conditions. Motivated by Chatelain, Choulli, and Henrot, 1996, we show in case the equality holds in the… (More)

- Kenneth S. Berenhaut, Colin Adams, John V. Baxley, Arthur T. Benjamin, Martin Bohner, Nigel Boston +56 others
- 2013

- Kenneth S. Berenhaut, John V. Baxley, Arthur T. Benjamin, Martin Bohner, Nigel Boston, Amarjit S. Budhiraja +45 others
- 2009

See inside back cover or http://pjm.math.berkeley.edu/involve for submission instructions and subscription prices. Subscriptions, requests for back issues from the last three years and changes of subscribers address should be sent to Mathematical Sciences Publishers, Generating and zeta functions, structure, spectral and analytic properties of the moments… (More)

- Kenneth S. Berenhaut, John V. Baxley, Arthur T. Benjamin, Martin Bohner, Nigel Boston, Amarjit S. Budhiraja +45 others
- 2009

See inside back cover or http://pjm.math.berkeley.edu/involve for submission instructions and subscription prices. Subscriptions, requests for back issues from the last three years and changes of subscribers address should be sent to Mathematical Sciences Publishers, Generating and zeta functions, structure, spectral and analytic properties of the moments… (More)

In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be… (More)

- GILES AUCHMUTY, BEHROUZ EMAMIZADEH, MOHSEN ZIVARI

This note extends the results in [2], by describing the dependence of the optimal constant in the p-version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.

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