On some properties of the class of stationary sets

Pascal Lefevre

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Endpoint bounds for convolution operators with singular measures

E. Ferreyra, T. Godoy, M. Urciuolo (1998)

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Let $S \subset ℝ^{n + 1}$ be the graph of the function $ϕ : {[- 1, 1]}^{n} \to ℝ$ defined by $ϕ (x_{1}, \dots, x_{n}) = \sum_{j = 1}^{n} {| x_{j} |}^{β_{j}},$ with 1< $β_{1} \leq \dots \leq β_{n},$ and let $μ$ the measure on $ℝ^{n + 1}$ induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with $μ$ is $L^{p}$ - $L^{q}$ bounded.

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...