A borderline case of Calderón-Zygmund estimates for nonuniformly elliptic problems
Algebra i analiz, Tome 31 (2019) no. 3, pp. 82-115.

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In a borderline case which was not covered before, nonlinear Calderón-Zygmund estimates are shown to be valid for a class of nonuniformly elliptic problems driven by double phase energies.
Keywords: Calderón–Zygmund estimates, nonuniformly elliptic problems, Lavrent'ev phenomenon, Euler–Lagrange equations, $p$-Laplacian, homogenization.
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C. De Filippis; G. Mingione. A borderline case of Calderón-Zygmund estimates for nonuniformly elliptic problems. Algebra i analiz, Tome 31 (2019) no. 3, pp. 82-115. http://geodesic.mathdoc.fr/item/AA_2019_31_3_a4/

[1] Avelin B., Kuusi T., Mingione G., “Nonlinear Calderón–Zygmund theory in the limiting case”, Arch. Ration. Mech. Anal., 227:2 (2018), 663–714

[2] Baroni P., Colombo M., Mingione G., “Harnack inequalities for double phase functionals”, Nonlinear Anal., 121 (2015), 206–222

[3] Baroni P., Colombo M., Mingione G., “Nonautonomous functionals, borderline cases and related function classes”, Algebra i analiz, 27:3 (2015), 6–50

[4] Baroni P., Colombo M., Mingione G., “Regularity for general functionals with double phase”, Calc. Var. Partial Differential Equations, 57:2 (2018), 62

[5] Byun S. S., Oh J., “Global gradient estimates for non-uniformly elliptic equations”, Calc. Var. Partial Differential Equations, 56:2 (2017), 46

[6] Byun S. S., Oh J., “Global gradient estimates for the borderline case of double phase problems with BMO coefficients in nonsmooth domains”, J. Differential. Equations, 263:2 (2017), 1643–1693

[7] Byun S. S., Ok J., Ryu S., “Global gradient estimates for elliptic equations of $p(x)$-Laplacian type with BMO nonlinearity”, Reine Angew. Math., 715 (2016), 1–38

[8] Choe H. J., “Interior behaviour of minimizers for certain functionals with nonstandard growth”, Nonlinear Anal., 19:10 (1992), 933–945

[9] Colombo M., Mingione G., “Regularity for double phase variational problems”, Arch. Rat. Mech. Anal., 215:2 (2015), 443–496

[10] Colombo M., Mingione G., “Bounded minimisers of double phase variational integrals”, Arch. Ration. Mech. Anal., 218:1 (2015), 219–273

[11] Colombo M., Mingione G., “Calderón–Zygmund estimates and non-uniformly elliptic operators”, J. Funct. Anal., 270:4 (2016), 1416–1478

[12] De Filippis C., “Higher integrability for constrained minimizers of integral functionals with $(p, q)$-growth in low dimension”, Nonlinear Anal., 170 (2018), 1–20

[13] De Filippis C.,, “Partial regularity for manifold constrained p(x)-harmonic maps”, Calc. Var. Partial Differential Equations, 58:2 (2019), 47 | DOI

[14] De Filippis C., Oh J., “Regularity for multi-phase variational problems”, J. Differential Equations, 2019 (to appear) | DOI

[15] Di Nezza E., Palatucci G., Valdinoci E., “Hitchiker's guide to the fractional Sobolev spaces”, Bull. Sci. Math., 136:5 (2012), 521–573

[16] Esposito L., Leonetti F., Mingione G., “Sharp regularity for functionals with $(p,q)$ growth”, J. Differential Equations, 204:1 (2004), 5–55

[17] Giusti E., Direct methods in the calculus of variations, World Sci. Publ. Co., Inc., River Edge, NJ, 2003

[18] Harjulehto P., Hästö P., Boundary regularity under generalized growth conditions, Preprint, 2017

[19] Harjulehto P., Hästö P., Toivanen O., “Hölder regularity of quasiminimizers under generalized growth conditions”, Calc. Var. Partial Differential Equations, 56:2 (2017), 22

[20] Hästö P., “The maximal operator on generalized Orlicz spaces”, J. Funct. Anal., 269:12 (2015), 4038–4048

[21] Kuusi T., Mingione G., “Guide to nonlinear potential estimates”, Bull. Math. Sci., 4:1 (2014), 1–82

[22] Kuusi T., Mingione G., “Vectorial nonlinear potential theory”, J. Eur. Math. Soc. (JEMS), 20:4 (2018), 929–1004

[23] Kuusi T., Mingione G., Sire Y., “Nonlocal self-improving properties”, Anal. PDE, 8:1 (2015), 57–114

[24] Lieberman G. M., “Boundary regularity for solutions of degenerate elliptic equations”, Nonlinear Anal., 12:11 (1988), 1203–1219

[25] Lieberman G. M., “The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations”, Comm. Partial Differential Equations, 16:2–3 (1991), 311–361

[26] Marcellini P., “Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions”, Arch. Rat. Mech. Anal., 105:3 (1989), 267–284

[27] Marcellini P., “Regularity and existence of solutions of elliptic equations with $p,q$-growth conditions”, J. Differential Equations, 90:1 (1991), 1–30

[28] Mingione G., “Bounds for the singular set of solutions to nonlinear elliptic systems”, Calc. Var. Partial Differential Equations, 18:4 (2003), 373–400

[29] Ok J., “Gradient estimates for elliptic equations with $L^{p(~\cdot~)}\log L$ growth”, Calc. Var. Partial Differential Equations, 55:2 (2016), 26

[30] Ok J., “Regularity of $\omega$-minimizers for a class of functionals with nonstandard growth”, Calc. Var. Partial Differential Equations, 56:2 (2017), 48

[31] Ragusa M. A., Tachikawa A., “Partial regularity of $p(x)$-harmonic maps”, Trans. Amer. Math. Soc., 365:6 (2013), 3329–3353

[32] Tachikawa A., Usuba S., “Regularity results up to the boundary for minimizers of $p(x)$-energy with $p(x)>1$”, Manuscripta Math., 152:1–2 (2017), 127–151

[33] Uhlenbeck K., “Regularity for a class of nonlinear elliptic systems”, Acta Math., 138:3–4 (1977), 219–240

[34] Uraltseva N. N., “Vyrozhdayuschiesya kvazilineinye ellipticheskie sistemy”, Zap. nauch. semin. LOMI, 7, 1968, 184–222

[35] Uraltseva N. N., Urdaletova A. B., “Ogranichennost gradientov obobschennykh reshenii vyrozhdayuschikhsya neravnomerno ellipticheskikh kvazilineinykh uravnenii”, Vestn. Leningr. un-ta. Ser. mat., mekh., astronom., 1983, no. 19, 50–56

[36] Zhikov V. V., “Usrednenie funktsionalov variatsionnogo ischisleniya i teorii uprugosti”, Izv. AN SSSR. Ser. mat., 50:4 (1986), 675–710

[37] Zhikov V. V., “On Lavrentiev's Phenomenon”, Russian J. Math. Phys., 3:2 (1995), 249–269

[38] Zhikov V. V., “On some variational problems”, Russian J. Math. Phys., 5:1 (1997), 105–116