singularities of solutions to equations of mathematical physics - mazija, kozlov.

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1、ContentsIntroduction1Part1.Singularitiesofsolutionstoequationsofmathematicalphysics7Chapter1.Prerequisitesonoperatorpencils91.1.Operatorpencils101.2.Operatorpencilscorrespondingtosesquilinearforms151.3.Avariationalprincipleforoperatorpencils211.4.Ellipticboun

2、daryvalueproblemsindomainswithconicpoints:somebasicresults261.5.Notes31Chapter2.Angleandconicsingularitiesofharmonicfunctions352.1.BoundaryvalueproblemsfortheLaplaceoperatorinanangle362.2.TheDirichletproblemfortheLaplaceoperatorinacone402.3.TheNeumannproblemf

3、ortheLaplaceoperatorinacone452.4.Theproblemwithobliquederivative492.5.Furtherresults522.6.ApplicationstoboundaryvalueproblemsfortheLaplaceequation542.7.Notes57Chapter3.TheDirichletproblemfortheLam¶esystem613.1.TheDirichletproblemfortheLam¶esysteminaplaneangle

4、643.2.TheoperatorpencilgeneratedbytheDirichletprobleminacone743.3.Propertiesofrealeigenvalues833.4.Thesetfunctions¡andFº883.5.Avariationalprincipleforrealeigenvalues913.6.Estimatesforthewidthoftheenergystrip933.7.Eigenvaluesforcircularcones973.8.Applications1

5、003.9.Notes105Chapter4.OtherboundaryvalueproblemsfortheLam¶esystem1074.1.AmixedboundaryvalueproblemfortheLam¶esystem1084.2.TheNeumannproblemfortheLam¶esysteminaplaneangle1204.3.TheNeumannproblemfortheLam¶esysteminacone1254.4.Angularcrackinananisotropicelastic

6、space1334.5.Notes138Chapter5.TheDirichletproblemfortheStokessystem139iiiCONTENTS5.1.TheDirichletproblemfortheStokessysteminanangle1425.2.TheoperatorpencilgeneratedbytheDirichletprobleminacone1485.3.Propertiesofrealeigenvalues1555.4.Theeigenvalues¸=1and¸={2159

7、5.5.Avariationalprincipleforrealeigenvalues1685.6.Eigenvaluesinthecaseofrightcircularcones1755.7.TheDirichletproblemfortheStokessysteminadihedron1785.8.StokesandNavier{Stokessystemsindomainswithpiecewisesmoothboundaries1925.9.Notes196Chapter6.Otherboundaryval

8、ueproblemsfortheStokessysteminacone1996.1.AmixedboundaryvalueproblemfortheStokessystem2006.2.Realeigenvaluesofthepenciltothemixedproblem2126.3.TheNeumannproblemfortheStokessystem2236.4.No