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Regularity of the homogeneous Monge-Ampère equation
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Characterization of function spaces via low regularity mollifiers
Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
1. | Departamento de Análisis Matemático, Universidad de Granada, Avenida Fuentenueva S/N, 18071 GRANADA, Spain |
2. | Department of Mathematics, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain, Spain, Spain |
  The main goal of this work is to study existence, uniqueness and summability of the solution $u$ with respect to the summability of the datum $f$. In the process we establish an $L^p$-theory, for $p \geq 1$, associated to these problems and we prove some useful inequalities for the applications.
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T.Kuusi, G.Mingione and Y. Sire, Nonlocal equations with measure data,, Preprint available at cvgmt.sns.it., (). Google Scholar |
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Nonlinear Phenomena in Ocean Dynamics (Los Alamos, NM, 1995), Phys. D., 98 (1996), 515-522.
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Second edition, Grundlehren der Mathematischen Wissenschaften, 342, Springer, Heidelberg, 2011.
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Comm. Pure Appl. Math., 13 (1960), 457-468.
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Annali di Matematica Pura ed Applicata, 192 (2013), 673-718.
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Ann. Scuola. Norm. Pisa., 11 (1910), p144. |
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Calc. Var. Partial Differential Equations, 50 (2014), 723-750.
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J. Math. Pures Appl., 101 (2014), 275-302.
doi: 10.1016/j.matpur.2013.06.003. |
[50] |
J. Geom. Anal., 19 (2009), 420-432.
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[51] |
J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
[52] |
Rendiconti di Matematica e delle sue applicazioni, 18 (1959), 95-139. |
[53] |
Communications on Pure and Applied Mathematics, 60 (2007), 67-112.
doi: 10.1002/cpa.20153. |
[54] |
Indiana Univ. Math. J., 55 (2006), 1155-1174.
doi: 10.1512/iumj.2006.55.2706. |
[55] |
J. Funct. Anal., 256 (2009), 1842-1864.
doi: 10.1016/j.jfa.2009.01.020. |
[56] |
Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258.
doi: 10.5802/aif.204. |
[57] |
Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J. 1970. |
[58] |
J. Math. Mech., 7 (1958), 503-514. |
[59] |
Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. |
[60] |
Pure and Applied Mathematics, Vol. IV. Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. |
[61] |
Mathematical Surveys and Monographs, 81, American Mathematical Society, Providence, RI, 2000. |
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J. Funct. Anal., 145 (1997), 136-150.
doi: 10.1006/jfan.1996.3016. |
[63] |
Bol. Soc. Esp. Mat. Apl. $S\veceMA$, 49 (2009), 33-44. |
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Dokl. Akad. Nauk SSSR, 97 (1954), 193-196. |
show all references
References:
[1] |
Ann. di Mat. Pura e Applicata, 182 (2003), 247-270.
doi: 10.1007/s10231-002-0064-y. |
[2] |
Pure and Applied Mathematics, Vol. 65, Academic Press, New York-London, 1975. |
[3] |
C. R. Math. Acad. Sci. Paris, 348 (2010), 759-762.
doi: 10.1016/j.crma.2010.05.006. |
[4] |
Math. Ann., 310 (1998), 527-560.
doi: 10.1007/s002080050159. |
[5] |
Nonlinear Ana. T.M.P., 32 (1998), 819-830.
doi: 10.1016/S0362-546X(97)00530-0. |
[6] |
$2^{nd}$ edition, Cambridge Studies in Advanced Mathematics, 116, Cambridge University Press, Cambridge, 2009.
doi: 10.1017/CBO9780511809781. |
[7] |
Arch. Rational Mech. Anal., 25 (1967), 81-122.
doi: 10.1007/BF00281291. |
[8] |
Trans. Amer. Math. Soc., 361 (2009), 1963-1999.
doi: 10.1090/S0002-9947-08-04544-3. |
[9] |
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, in press, corrected proof, available online 2 May 2014.
doi: 10.1016/j.anihpc.2014.04.003. |
[10] |
Commun. Contemp. Math., 16 (2014), 1350046, 29 pp.
doi: 10.1142/S0219199713500466. |
[11] |
Advances in Nonlinear Analysis, Published online February 2015.
doi: 10.1515/anona-2015-0012. |
[12] |
Adv. Math. Sci. Appl., 9 (1999), 1017-1031. |
[13] |
J. Funct. Anal., 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0. |
[14] |
Nonlinear Anal., 71 (2009), 978-990.
doi: 10.1016/j.na.2008.11.066. |
[15] |
Quaderni dell'UMI. 51, Bologna, 2010. Google Scholar |
[16] |
Kodai Math. J., 37 (2014), 769-799.
doi: 10.2996/kmj/1414674621. |
[17] |
Manuscripta Math., 74 (1992), 87-106.
doi: 10.1007/BF02567660. |
[18] |
J. Evol. Equ., 1 (2001), 387-404.
doi: 10.1007/PL00001378. |
[19] |
Nonlinear Anal., 10 (1986), 55-64.
doi: 10.1016/0362-546X(86)90011-8. |
[20] |
Comm. Pure Appl. Math., 58 (2005), 1678-1732.
doi: 10.1002/cpa.20093. |
[21] |
Comm. Math. Phys., 320 (2013), 679-722.
doi: 10.1007/s00220-013-1682-5. |
[22] |
Comm. Partial Differential Equations, 4 (1979), 1067-1075.
doi: 10.1080/03605307908820119. |
[23] |
J. Eur. Math. Soc., 12 (2010), 1151-1179.
doi: 10.4171/JEMS/226. |
[24] |
Annals of Mathematics. Second Series, 171 (2010), 1903-1930.
doi: 10.4007/annals.2010.171.1903. |
[25] |
Quaderni Scuola Normale Superiore di Pisa, Pisa, 1980. |
[26] |
Wave Motion, 19 (1994), 367-389.
doi: 10.1016/0165-2125(94)90003-5. |
[27] |
Ann. Inst. H. Poincare, Anal. Non Lineaire, 14 (1997), 615-667.
doi: 10.1016/S0294-1449(97)80128-X. |
[28] |
5, Springer-Verlag, 1992.
doi: 10.1007/978-3-642-58090-1. |
[29] |
J. Funct. Anal., 267 (2014), 1807-1836.
doi: 10.1016/j.jfa.2014.05.023. |
[30] |
Bull. Sci. Math., 136 (2012), 521-573.
doi: 10.1016/j.bulsci.2011.12.004. |
[31] |
Commun. Math. Phys., 333 (2015), 1061-1105.
doi: 10.1007/s00220-014-2118-6. |
[32] |
Comm. PDE, 38 (2013), 1539-1573.
doi: 10.1080/03605302.2013.808211. |
[33] |
J. Amer. Math. Soc., 21 (2008), 925-950.
doi: 10.1090/S0894-0347-07-00582-6. |
[34] |
Publ. RIMS, Kyoto Univ., 13 (1977), 277-284.
doi: 10.2977/prims/1195190108. |
[35] |
Reprint of the 1994 edition, Classics in Mathematics, Springer, Berlin, 2007. |
[36] |
Publ. Mat., 55 (2011), 151-161.
doi: 10.5565/PUBLMAT_55111_07. |
[37] |
Calc. Var., 34 (2009), 1-21.
doi: 10.1007/s00526-008-0173-6. |
[38] |
Bound. Value Probl., 2007, Art. ID 81415, 21 pp. |
[39] |
T.Kuusi, G.Mingione and Y. Sire, Nonlocal equations with measure data,, Preprint available at cvgmt.sns.it., (). Google Scholar |
[40] |
Ann. of Math., 118 (1983), 349-374.
doi: 10.2307/2007032. |
[41] |
Nonlinear Phenomena in Ocean Dynamics (Los Alamos, NM, 1995), Phys. D., 98 (1996), 515-522.
doi: 10.1016/0167-2789(96)00114-5. |
[42] |
Second edition, Grundlehren der Mathematischen Wissenschaften, 342, Springer, Heidelberg, 2011.
doi: 10.1007/978-3-642-15564-2. |
[43] |
Comm. Pure Appl. Math., 13 (1960), 457-468.
doi: 10.1002/cpa.3160130308. |
[44] |
(eds. L. Bers, F. John and M. Schechter), Lectures in Applied Mathematics, Vol. III, Interscience New York, 1964. |
[45] |
Calc. Var. Partial Differential Equations, 50 (2014), 799-829.
doi: 10.1007/s00526-013-0656-y. |
[46] |
Annali di Matematica Pura ed Applicata, 192 (2013), 673-718.
doi: 10.1007/s10231-011-0243-9. |
[47] |
Ann. Scuola. Norm. Pisa., 11 (1910), p144. |
[48] |
Calc. Var. Partial Differential Equations, 50 (2014), 723-750.
doi: 10.1007/s00526-013-0653-1. |
[49] |
J. Math. Pures Appl., 101 (2014), 275-302.
doi: 10.1016/j.matpur.2013.06.003. |
[50] |
J. Geom. Anal., 19 (2009), 420-432.
doi: 10.1007/s12220-008-9064-5. |
[51] |
J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
[52] |
Rendiconti di Matematica e delle sue applicazioni, 18 (1959), 95-139. |
[53] |
Communications on Pure and Applied Mathematics, 60 (2007), 67-112.
doi: 10.1002/cpa.20153. |
[54] |
Indiana Univ. Math. J., 55 (2006), 1155-1174.
doi: 10.1512/iumj.2006.55.2706. |
[55] |
J. Funct. Anal., 256 (2009), 1842-1864.
doi: 10.1016/j.jfa.2009.01.020. |
[56] |
Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258.
doi: 10.5802/aif.204. |
[57] |
Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J. 1970. |
[58] |
J. Math. Mech., 7 (1958), 503-514. |
[59] |
Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. |
[60] |
Pure and Applied Mathematics, Vol. IV. Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. |
[61] |
Mathematical Surveys and Monographs, 81, American Mathematical Society, Providence, RI, 2000. |
[62] |
J. Funct. Anal., 145 (1997), 136-150.
doi: 10.1006/jfan.1996.3016. |
[63] |
Bol. Soc. Esp. Mat. Apl. $S\veceMA$, 49 (2009), 33-44. |
[64] |
Dokl. Akad. Nauk SSSR, 97 (1954), 193-196. |
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