Displaying similar documents to “Local monotonicity of Hausdorff measures restricted to curves in ℝ n ”

Continuity of monotone functions

Boris Lavrič (1993)

Archivum Mathematicum

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It is shown that a monotone function acting between euclidean spaces R n and R m is continuous almost everywhere with respect to the Lebesgue measure on R n .

Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

Ralf Bader, Nikolaos Papageorgiou (2000)

Annales Polonici Mathematici

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We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of...

Concentrated monotone measures with non-unique tangential behavior in ℝ 3

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

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We show that for every ε > 0 there is a set A ⊂ ℝ 3 such that ℋ 1 ⌞ A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and ℋ 1 ⌞ A has the 1 -dimensional density between 1 and 2 + ε everywhere in the support.