On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems

Dung Le

doi:10.3934/dcdsb.2014.19.3245

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2014, Volume 19, Issue 10: 3245-3265. Doi: 10.3934/dcdsb.2014.19.3245

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On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems

Dung Le^1,

1.
Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249

Received: June 30, 2013

Revised: September 30, 2013

Published: November 2014

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Abstract

This paper studies Holder continuity of weak solutions to strongly coupled elliptic systems. We do not assume that the solutions are bounded but BMO and the ellipticity constants can be unbounded.

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Mathematics Subject Classification: Primary: 35J70, 35B65; Secondary: 42B37.

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References

[1]	B. Franchi, C. Perez and R. L. Wheeden, Self-Improving Properties of John Nirenberg and Poincaré Inequalities on Spaces of Homogeneous Type, J. Functional Analysis, 153 (1998), 108-146.doi: 10.1006/jfan.1997.3175.
[2]	E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2003.doi: 10.1142/9789812795557.
[3]	R. L. Johnson and C. J. Neugebauer, Properties of BMO functions whose reciprocals are also BMO, Z. Anal. Anwendungen, 12 (1993), 3-11.
[4]	D. Le, Regularity of BMO weak solutions to nonlinear parabolic systems via homotopy, Transactions of AMS, 365 (2013), 2723-2753.doi: 10.1090/S0002-9947-2012-05720-5.
[5]	D. Le, Everywhere regularity of BMO weak solutions to uniform elliptic systems, submitted.
[6]	D. Le, L. Nguyen and T. Nguyen, Coexistence in Cross Diffusion systems, Indiana Univ. J. Math., 56 (2007), 1749-1791.
[7]	J. Orobitg and C. Pérez, $A_p$ weights for nondoubling measures in $\RR^n$ and applications, Transactions of AMS, 354 (2002), 2013-2033.doi: 10.1090/S0002-9947-02-02922-7.
[8]	E. M. Stein, Harmonic Analysis, Real Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, NJ, 1993.