-regularity theory of linear strongly elliptic Dirichlet systems of order with minimal regularity in the coefficients

Author:
Stefan Ebenfeld

Journal:
Quart. Appl. Math. **60** (2002), 547-576

MSC:
Primary 35J55; Secondary 35B45, 35B65

DOI:
https://doi.org/10.1090/qam/1914441

MathSciNet review:
MR1914441

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Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we consider the following Dirichlet system of order :

**[1]**R. Adams,*Sobolev Spaces*, Academic Press, New York, 1975 MR**0450957****[2]**S. Agmon,*Lectures on Elliptic Boundary Value Problems*, Van Nostrand, Princeton, NJ, 1965 MR**0178246****[3]**S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions 1, Comm. Pure Appl. Math.**12**, 623-727 (1959) MR**0125307****[4]**S. Agmon, A. Douglis, and L. Nirenberg,*Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions*2, Comm. Pure Appl. Math.**17**, 35-92 (1964) MR**0162050****[5]**C. Bandle and M. Flucher,*Table of Inequalities in Elliptic Boundary Value Problems*, Math. Appl., Vol. 430, Kluwer, Dordrecht, 1998 MR**1609927****[6]**C. Dafermos and W. Hrusa,*Energy methods for quasilinear hyperbolic initial-boundary value problems*, Arch. Rational Mech. Anal.**87**, 267-292 (1985) MR**768069****[7]**S. Ebenfeld,*Aspekte der Kontinua mit Mikrostruktur*, Ph.D. thesis, Darmstadt, Shaker-Verlag, 1998**[8]**M. Giaquinta,*Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems*, Princeton University Press, 1983 MR**717034****[9]**D. Gilbarg and N. Trudinger,*Elliptic Partial Differential Equations of Second Order*, Springer, 1983 MR**737190****[10]**T. Kato,*Abstract Evolution Equations and Nonlinear Mixed Problems*, Lezioni Fermiane Pisa, 1988**[11]**H. Koch,*Hyperbolic Equations of Second Order*, Ph.D. thesis, Heidelberg, 1990**[12]**H. Koch,*Mixed problems for fully nonlinear hyperbolic problems*, Math. Zeit.**214**, 9-42 (1993) MR**1234595****[13]**A. Koshelev,*Regularity Problem for Quasilinear Elliptic and Parabolic Systems*, Springer-Verlag, New York, 1995 MR**1442954****[14]**A. Milani,*A Regularity Result for Strongly Elliptic Systems*, Bollettino Un. Mat. Ital. B**2**, 641-651 (1983) MR**716753****[15]**A. Milani,*A remark on the Sobolev regularity of classical solutions to strongly elliptic equations*, Math. Nachr.**190**, 203-219 (1998) MR**1611620****[16]**C. B. Morrey,*Multiple Integrals in the Calculus of Variations*, Springer, 1966**[17]**M. Renardy and R. Rogers,*An Introduction to Partial Differential Equations*, Springer-Verlag, New York, 1992 MR**2028503****[18]**J. Wloka,*Partielle Differentialgleichungen*, Sobolevräume und Randwertaufgaben, Teubner, Stuttgart, 1982 MR**652934**

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Additional Information

DOI:
https://doi.org/10.1090/qam/1914441

Article copyright:
© Copyright 2002
American Mathematical Society