Square Roots of Elliptic Systems in Locally Uniform Domains

Introduction.- Locally uniform domains.- A density result for locally uniform domains.- Sobolev extension operator.- A short account on sectorial and bisectorial operators.- Elliptic systems in divergence form.- Porous sets.- Sobolev spaces with a vanishing trace condition.- Hardy's inequality.- Real interpolation of Sobolev spaces.- Higher regularity for fractional powers of the Laplacian.- First order formalism.- Kato's square root property on thick sets.- Removing the thickness condition.- Interlude: Extension operators for fractional Sobolev spaces.- Critical numbers and Lp ? Lq bounded families of operators.- Lp-bounds for the H1-calculus and Riesz transform.- Calder?on-Zygmund decomposition for Sobolev functions.- Lp bounds for square roots of elliptic systems.- References.- Index.

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• Análise real, variáveis ??reais
• Análise funcional e transforma
• Cálculo diferencial e equações

Mixed Boundary Conditions;Function Spaces;Extension Operators;Hardy's Inequality;Kato's Square Root Problem;Riesz Transforms;Fractional Laplacian;Functional Calculus;Sobolev Spaces;Interpolation Theory