04869nam 22008173 450 991096076020332120231110232504.097814704691531470469154(MiAaPQ)EBC6852911(Au-PeEL)EBL6852911(CKB)20667666500041(RPAM)22491296(OCoLC)1295277368(EXLCZ)992066766650004120220117d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierElliptic Theory for Sets with Higher Co-Dimensional Boundaries1st ed.Providence :American Mathematical Society,2022.©2021.1 online resource (136 pages)Memoirs of the American Mathematical Society ;v.274"November 2021, volume 274."Print version: David, Guy Elliptic Theory for Sets with Higher Co-Dimensional Boundaries Providence : American Mathematical Society,c2022 9781470450434 Includes bibliographical references.The Harnack chain condition and the doubling property -- Traces -- Poincaré inequalities -- Completeness and density of smooth functions -- The chain rule and applications -- The extension operator -- Definition of solutions -- Harmonic measure -- Green functions -- The comparison principle."Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1"--Provided by publisher.Memoirs of the American Mathematical Society Differential equations, EllipticDegenerate differential equationsHarmonic functionsHarmonic analysisBoundary value problemsPotential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functionsmscPartial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equationsmscMeasure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theorymscMeasure and integration -- Classical measure theory -- Hausdorff and packing measuresmscPartial differential equations -- Elliptic equations and systems -- Degenerate elliptic equationsmscHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.)mscHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theorymscHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDEmscDifferential equations, Elliptic.Degenerate differential equations.Harmonic functions.Harmonic analysis.Boundary value problems.Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions.Partial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations.Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory.Measure and integration -- Classical measure theory -- Hausdorff and packing measures.Partial differential equations -- Elliptic equations and systems -- Degenerate elliptic equations.Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.).Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE.518/.6431B0535J2528A7528A7835J7042B2042B2542B37mscDavid Guy350534Feneuil Joseph1802032Mayboroda Svitlana1802033MiAaPQMiAaPQMiAaPQBOOK9910960760203321Elliptic Theory for Sets with Higher Co-Dimensional Boundaries4347557UNINA