×

zbMATH — the first resource for mathematics

Dirichlet problem for parabolic equations with continuous coefficients. (English) Zbl 0336.35056
MSC:
35K25 Higher-order parabolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B45 A priori estimates in context of PDEs
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] S. Agmon - A. Douglis - L. Nirenberg , Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I , Communications on Pure and Applied Mathematics , 12 , no. 4 ( 1959 ). MR 125307 | Zbl 0093.10401 · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[2] E.B. Pabes , Singular integrals and partial differential equations of parabolic type , Studia Mathematica , 28 ( 1966 ). Article | MR 213744 | Zbl 0144.35002 · Zbl 0144.35002 · eudml:217213
[3] E.B. Fabes - M. Jodeit Jr. , LP-boundary value problems for parabolic equations , Bulletin A.M.S. , 74 , no. 6 ( 1968 ). Also Singular integrals and boundary value problems for parabolic equations in a half-space, University of Minnesota. MR 233081 | Zbl 0174.42202 · Zbl 0174.42202 · doi:10.1090/S0002-9904-1968-12061-0
[4] E.B. Fabes - N.M. Rivière , Systems of parabolic equations with uniformly continuous coefficients , Journal d’Analyse Mathématique , 17 ( 1966 ). MR 216137 | Zbl 0144.35203 · Zbl 0144.35203 · doi:10.1007/BF02788662
[5] E.B. Fabes - N.M. Rivière , LP-estimates near the boundary for solutions of the Dirichlet problem , Annali della Scuola Normale Superiore , Pisa , 24 , fasc. III ( 1970 ). Numdam | MR 287142 | Zbl 0207.10503 · Zbl 0207.10503 · numdam:ASNSP_1970_3_24_3_491_0 · eudml:83537
[6] E.B. Fabes , Singular integrals and their applications to the Cauchy and Cauchy-Dirichlet problems for parabolic equations , Notes from a course given at the Istituto Matematico , Università di Ferrara , Italia, 1970 .
[7] A. Friedman , Partial Differential Equations of Parabolic Type , Prentice-Hall, Inc. , Englewood Cliffs, N. J. , 1964 . MR 181836 | Zbl 0144.34903 · Zbl 0144.34903
[8] G.H. Hardy - J.E. Littlewood - G. Pölya , Inequalities , Cambridge at the University Press , 1952 . MR 46395 | Zbl 0047.05302 · Zbl 0047.05302
[9] E.M. Stein , Singular Integrals and Differentiability Properties of Functions , Princeton University Press , 1970 . MR 290095 | Zbl 0207.13501 · Zbl 0207.13501
[10] V.A. Solonnikov , On boundary value problems for linear parabolic systems of differential equations of a general type (Russian) , Trudy Matematicheskogo Instituta Akademii Nauk (Steklov), 83 , Leningrad , 1965 . MR 211083 | Zbl 0164.12502 · Zbl 0164.12502
[11] E. Gagliardo , Proprietà di alcune classi di funzioni di più variabili , Ricerche di Matematica , 7 ( 1958 ). MR 102740 | Zbl 0089.09401 · Zbl 0089.09401
[12] W. Pogorzelski , Étude de la matrice des solutions fondamentales du système parabolique d’équations aux dérivées partielles , Ricerche di Matematica , 7 ( 2 ) ( 1958 ). MR 105561 | Zbl 0085.30903 · Zbl 0085.30903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.