"Harmonic Analysis and PDE 001.ps.gz" - читать интересную книгу автораHARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS BJO"RN E. J. DAHLBERG CARLOS E. KENIG ISSN 0347-2809 DEPARTMENT OF MATHEMATICS CHALMERS UNIVERSITY OF TECHNOLOGY AND THE UNIVERSITY OF GO"TEBORG GO"TEBORG 1985/1996 FOREWORD These lecture notes are based on a course I gave first at University of Texas, Austin during the academic year 1983 - 1984 and at University of Go"teborg in the fall of 1984. My purpose in those lectures was to present some of the required background in order to present the recent results on the solvability of boundary value problems in domains with "bad" boundaries. These notes concentrate on the boundary value problems for the Laplace operator; for a complete survey of results, we refer to the survey article by Carlos Kenig; I am very grateful for this kind permission to include it here. It is also my pleasure to acknowledge my gratitude to Peter Kumlin for excellent work in preparing these notes for publication. January 1985 Bjo"rn E. J. Dahlberg Contents 0 Introduction 1 1 Dirichlet Problem for Lipschitz Domain. The Setup 11 2 Proofs of Theorem 1.1 and Theorem 1.2 19 3 Proof of Theorem 1.6 25 4 Proof of Theorem 1.3 37 5 Proof of Theorem 1.4 47 6 Dirichlet Problem for Lipschitz domains. The final arguments for the L2-theory 51 7 Existence of solutions to Dirichlet and Neumann problems for Lipschitz domains. The optimal Lp-results 57 Index : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 64 Appendix 1 C. E. Kenig: Recent Progress on Boundary Value Problems on Lipschitz Domains : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 67 Appendix 2 B. E. Dahlberg/C. E. Kenig: Hardy spaces and the Neumann Problem in Lp for Laplace's equation in Lipschitz domains : : : : : : : : : 107 iii iv |
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