October  2015, 35(10): 4791-4804. doi: 10.3934/dcds.2015.35.4791

Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains

1. 

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea

2. 

School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, South Korea

Received  August 2014 Revised  February 2015 Published  April 2015

A global Calderón-Zygmund estimate type estimate in Weighted Lorentz spaces and Lorentz-Morrey spaces is obtained for weak solutions to elliptic obstacle problems of $p$-Laplacian type with discontinuous coefficients over Reifenberg flat domains.
Citation: Sun-Sig Byun, Yumi Cho. Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 4791-4804. doi: 10.3934/dcds.2015.35.4791
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show all references

References:
[1]

Nonlinear Anal., 96 (2014), 167-188. doi: 10.1016/j.na.2013.11.004.  Google Scholar

[2]

Pure and Applied Mathematics, 129, Academic Press, Inc., Boston, MA, 1988.  Google Scholar

[3]

Calc. Var. Partial Differential Equations, 2014. doi: 10.1007/s00526-014-0772-3.  Google Scholar

[4]

J. Reine Angew. Math., 650 (2011), 107-160. doi: 10.1515/CRELLE.2011.006.  Google Scholar

[5]

Calc. Var. Partial Differential Equations, 49 (2014), 37-76. doi: 10.1007/s00526-012-0574-4.  Google Scholar

[6]

Bull. London Math. Soc., 45 (2013), 765-778. doi: 10.1112/blms/bdt011.  Google Scholar

[7]

Proc. Amer. Math. Soc., (2015). doi: 10.1090/S0002-9939-2015-12458-6.  Google Scholar

[8]

J. Funct. Anal., 263 (2012), 3117-3143. doi: 10.1016/j.jfa.2012.07.018.  Google Scholar

[9]

J. Math. Anal. Appl., 372 (2010), 140-161. doi: 10.1016/j.jmaa.2010.05.072.  Google Scholar

[10]

Adv. Nonlinear Anal., 3 (2014), 15-44. doi: 10.1515/anona-2013-0024.  Google Scholar

[11]

Second edition, Robert E. Krieger Publishing Co. Inc., Malabar, FL, 1988.  Google Scholar

[12]

Graduate Texts in Mathematics, 250, Springer, New York, 2009. doi: 10.1007/978-0-387-09434-2.  Google Scholar

[13]

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 108 (2014), 733-755. doi: 10.1007/s13398-013-0137-3.  Google Scholar

[14]

Unabridged republication of the 1993 original, Dover Publications, Inc., Mineola, NY, 2006.  Google Scholar

[15]

J. Funct. Anal., 130 (1995), 161-219. doi: 10.1006/jfan.1995.1067.  Google Scholar

[16]

Math. Nachr., 287 (2014), 938-954. doi: 10.1002/mana.201200278.  Google Scholar

[17]

Reprint of the 1980 original, Classics in Applied Mathematics, 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. doi: 10.1137/1.9780898719451.  Google Scholar

[18]

Ann. of Math., 51 (1950), 37-55. doi: 10.2307/1969496.  Google Scholar

[19]

J. Differential Equations, 250 (2011), 2485-2507. doi: 10.1016/j.jde.2010.11.009.  Google Scholar

[20]

Arch. Ration. Mech. Anal., 203 (2012), 189-216. doi: 10.1007/s00205-011-0446-7.  Google Scholar

[21]

T. Mengesha and N. C. Phuc, Quasilinear Riccati type equations with distributional data in Morrey space framework,, , ().   Google Scholar

[22]

Ann. Scuola Norm. Sup. Pisa (3), 17 (1963), 189-206.  Google Scholar

[23]

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 6 (2007), 195-261.  Google Scholar

[24]

Advances in Computational Economics, 1, Kluwer Academic Publishers Group, Dordrecht, 1993. doi: 10.1007/978-94-011-2178-1.  Google Scholar

[25]

Adv. Math., 250 (2014), 387-419. doi: 10.1016/j.aim.2013.09.022.  Google Scholar

[26]

Acta Math., 104 (1960), 1-92. doi: 10.1007/BF02547186.  Google Scholar

[27]

North-Holland Mathematics Studies, 134, Notas de Matemática [Mathematical Notes], 114, North-Holland Publishing Co., Amsterdam, 1987.  Google Scholar

[28]

J. Funct. Anal., 262 (2012), 2777-2832. doi: 10.1016/j.jfa.2012.01.003.  Google Scholar

[29]

Manuscripta Math., 146 (2015), 7-63. doi: 10.1007/s00229-014-0684-8.  Google Scholar

[30]

Princeton Mathematical Series, 32, Princeton University Press, Princeton, NJ, 1971.  Google Scholar

[31]

Notices Amer. Math. Soc., 44 (1997), 1087-1094.  Google Scholar

[32]

Math. Nachr., 283 (2010), 1358-1367. doi: 10.1002/mana.200710084.  Google Scholar

[33]

J. Funct. Anal., 267 (2014), 605-642. doi: 10.1016/j.jfa.2014.03.022.  Google Scholar

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