Isoperimetric estimates for the first eigenvalue of the $p$-Laplace operator and the Cheeger constant

By B. Kawohl, V. Fridman. 2003

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View Paper: https://www.semanticscholar.org/paper/b176fc986739e7d833a5ae2299dc4a7e24929424

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Citations in the corpus

An overview on the Cheeger problem (2015, background): “We now focus on the Cheeger problem, and in doing so we first present some general properties of the Cheeger constant h(Ω) and of Cheeger sets inside Ω, valid for any dimension n ≥ 2 (see [34, 22, 23]).”
Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities (2009, methodology): “We start by showing, in the spirit of the argument in [13], that lim sup p→1+ λp,q(p)( ) ≤ hm( ) , (2.”
ON THE HIGHER EIGENVALUES FOR THE ∞-EIGENVALUE PROBLEM (2004, background): “The other extreme situation, the case p =1 , is studied in [ 16 ] by Fridman and Kawohl, see also the references therein.”
Overdetermined problems with possibly degenerate ellipticity, a geometric approach (2006, unknown): “According to [24] and [25] we say that Ω coincides with its Cheeger set if |∂Ω| |Ω| = min D |∂D| |D| := h(Ω)”
DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM (2007, background): “In two dimensions this follows from [31], and in higher dimensions one can first derive the result that almost all level sets of minimizers are Cheeger sets (see [28]) and then refer to results from [23] to verify that the boundary of Cheeger sets is piecewise smooth.”
Computing the first eigenvalue of the p-Laplacian via the inverse power method. (2009, background): “An important lower bound for λp(Ω) (see [7]) is λp(B) where B ⊂RN is a ball centered at the origin and with the same N -dimensional Lebesgue measure of Ω .”
AN INTRODUCTION TO THE CHEEGER PROBLEM (2011, unknown): “Another application concerns the asymptotic behaviour of the first eigenvalue of the p-Laplacian for p→ 1, as shown in [18].”