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1、Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/262919940HarnackInequalitiesandHeatKernelEstimatesforDegenerateDiffusionOperatorsArisinginPopulationBiologyArticleinAppliedMathematicsResearcheXpress·June2014DOI:10.1093/amr
2、x/abw002·Source:arXivCITATIONSREADS3172authors:CharlesEpsteinRafeMazzeoUniversityofPennsylvaniaStanfordUniversity90PUBLICATIONS1,705CITATIONS128PUBLICATIONS2,857CITATIONSSEEPROFILESEEPROFILEAllin-textreferencesunderlinedinbluearelinkedtopublicationsonResearchGate,Available
3、from:CharlesEpsteinlettingyouaccessandreadthemimmediately.Retrievedon:13October2016HarnackInequalitiesandHeat-kernelEstimatesforDegenerateDiffusionOperatorsArisinginPopulationBiologyCharlesL.Epstein∗andRafeMazzeo†June5,2014AbstractThispapercontinuestheanalysis,startedin[3,
4、4],ofaclassofdegener-ateellipticoperatorsdefinedonmanifoldswithcorners,whichariseinPop-ulationBiology.UsingtechniquespioneeredbyJ.Moser,andextendedandrefinedbyL.Saloff-Coste,Grigor'yan,andSturm,weshowthatweakso-lutionstotheparabolicproblemdefinedbyasub-classoftheseoperators,w
5、hichconsistsofthosethatcanbedefinedbyDirichletformsandhavenon-vanishingtransversevectorfield,satisfyaHarnackinequality.Thisallowsustoconcludethatthesolutionstotheseequationsbelong,forpositivetimes,tothenaturalanisotropicH¨olderspaces,andalsoleadstoupperand,insomecases,lowerb
6、oundsfortheheatkernelsoftheseoperators.Theseresultsim-plythattheseoperatorshaveacompactresolventwhenactingonC0orL2.TheproofreliesuponascaleinvariantPoincar´einequalitythatweestablishforalargeclassofweightedDirichletforms,aswellasestimatestohandlecertainmildlysingularpertur
7、bationterms.TheweightsthatweconsiderareneitherAhlforsregular,nordotheygenerallybelongtotheMuckenhauptclassA2.arXiv:1406.1426v1[math.AP]5Jun20141IntroductionInaseriesofpaperandabookwehaveconsideredtheanalysisofaclassofde-generatediffusionoperators,whichariseinPopulationBiol
8、ogy,whichwecall∗ResearchpartiallysupportedbyNSFgrantDMS12-05851,andAROgrantW911NF-12-1-05
