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Hardy’s inequality and curvature
, 2011
"... Abstract. A Hardy inequality of the form ∇f(x)  p ( ) p ∫ p − 1 dx ≥ {1 + a(δ, ∂Ω)(x)} p ..."
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Cited by 4 (2 self)
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Abstract. A Hardy inequality of the form ∇f(x)  p ( ) p ∫ p − 1 dx ≥ {1 + a(δ, ∂Ω)(x)} p
Spectral stability of the Neumann Laplacian
 J. Diff. Eq
"... We prove the equivalence of Hardy and Sobolevtype inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of th ..."
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Cited by 3 (0 self)
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We prove the equivalence of Hardy and Sobolevtype inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of the region within a uniform Hölder category then the eigenvalues of the Neumann Laplacian change by a small and explicitly estimated amount.
CHARACTERIZATIONS FOR HARDY’S INEQUALITY
"... We discuss necessary and sufficient conditions for validity of Hardy’s inequality. Assume that Ω is a proper open subset of Rn and let 1 < p < ∞. We say that pHardy’s inequality holds in Ω, if there is a ..."
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Cited by 2 (0 self)
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We discuss necessary and sufficient conditions for validity of Hardy’s inequality. Assume that Ω is a proper open subset of Rn and let 1 < p < ∞. We say that pHardy’s inequality holds in Ω, if there is a
Boundary decay estimates for solutions of elliptic equations
, 2008
"... We obtain integral boundary decay estimates for solutions of second and fourthorder elliptic equations on a bounded domain with smooth boundary. These improve upon previous results of this type in the secondorder case and, we believe, are new in the fourth order case. We apply these estimates to ..."
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We obtain integral boundary decay estimates for solutions of second and fourthorder elliptic equations on a bounded domain with smooth boundary. These improve upon previous results of this type in the secondorder case and, we believe, are new in the fourth order case. We apply these estimates to obtain stability bounds for the corresponding eigenvalues under small perturbations of the boundary. AMS Subject Classification: 35J40 (35P15)
unknown title
, 2007
"... Boundary decay estimates for solutions of fourthorder elliptic equations ..."
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Boundary decay estimates for solutions of fourthorder elliptic equations