1Abdellaoui, B., Attar, A. and Bentifour, R.. On the Fractional p-Laplacian equations with weight and general datum. Adv. Nonlinear Anal. 8 (2019), 144–174.
2Abdellaoui, B. and Bentifour, R.. Caffarelli–Kohn–Nirenberg type inequalities of fractional order with applications. J. Funct. Anal. 272 (2017), 3998–4029.
3Abdellaoui, B., Dall'Aglio, A. and Peral, I.. Some remarks on elliptic problems with critical growth in the gradient. J. Differ. Equ. 222 (2006), 21–62.
4Abdellaoui, B. and Peral, I.. Towards a deterministic KPZ equation with fractional diffusion: The stationary problem. Nonlinearity 31 (2018), 1260.
5Adams, R. A.. Sobolev spaces (New York: Academic Press, 1975).
6Applebaum, D., Lévy processes and stochastic calculus. Cambridge Studies in Advanced Mathematics, vol. 93 (Cambridge: Cambridge University Press, 2004).
7Arcoya, D., De Coster, C., Jeanjean, L. and Tanaka, K.. Continuum of solutions for an elliptic problem with critical growth in the gradient. J. Funct. Anal. 268 (2015), 2298–2335.
8Barrios, B., Figalli, A. and Ros-Oton, X.. Free boundary regularity in the parabolic fractional obstacle problem. Commun. Pure Appl. Math. 71 (2018), 2129–2159.
9Barrios, B., Figalli, A. and Ros-Oton, X.. Global regularity for the free boundary in the obstacle problem for the fractional Laplacian. Am. J. Math. 140 (2018), 415–447.
10Boccardo, L., Murat, F. and Puel, J.-P., Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique. In Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. IV (Paris, 1981/1982). Res. Notes in Math., vol. 84, pp. 19–73 (Boston, MA, London: Pitman, 1983).
11Bourgain, J., Brezis, H. and Mironescu, P., Another look at Sobolev spaces. In Optimal control and partial differential equations. pp. 439–455. (Amsterdam: IOS, 2001).
12Brezis, H. and Mironescu, P.. Gagliardo–Nirenberg inequalities and non-inequalities: The full story. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), 1355–1376.
13Caffarelli, L. and Dávila, G.. Interior regularity for fractional systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2018), 165–180.
14Caffarelli, L. and Figalli, A.. Regularity of solutions to the parabolic fractional obstacle problem. J. Reine Angew. Math. 680 (2013), 191–233.
15Caffarelli, L. and Vasseur, A.. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. 171 (2010), 1903–1930.
16Chen, H. and Véron, L.. Semilinear fractional elliptic equations involving measures. J. Differ. Equ. 257 (2014), 1457–1486.
17Chen, H. and Véron, L.. Semilinear fractional elliptic equations with gradient nonlinearity involving measures. J. Funct. Anal. 266 (2014), 5467–5492.
18Cont, R. and Tankov, P., Financial modelling with jump processes. Chapman & Hall/CRC Financial Mathematics Series (Boca Raton, FL: Chapman & Hall/CRC, 2004).
19Da Lio, F. and Rivière, T.. Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps. Adv. Math. 227 (2011), 1300–1348.
20Da Lio, F. and Schikorra, A.. n/p-Harmonic maps: Regularity for the sphere case. Adv. Calc. Var. 7 (2014), 1–26.
21De Coster, C. and Fernández, A. J.. Existence and multiplicity for elliptic p-Laplacian problems with critical growth in the gradient. Calc. Var. Partial Differ. Equ. 57 (2018), 89.
22Di Nezza, E., Palatucci, G. and Valdinoci, E.. Hitchhiker's guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012), 521–573.
23Dipierro, S., Figalli, A. and Valdinoci, E.. Strongly nonlocal dislocation dynamics in crystals. Commun. Partial Differ. Equ. 39 (2014), 2351–2387.
24Dipierro, S., Palatucci, G. and Valdinoci, E.. Dislocation dynamics in crystals: A macroscopic theory in a fractional Laplace setting. Commun. Math. Phys. 333 (2015), 1061–1105.
25Ferone, V. and Murat, F.. Nonlinear problems having natural growth in the gradient: An existence result when the source terms are small. Nonlinear Anal. Ser. A: Theory Methods) 42 (2000), 1309–1326.
26Ferrari, F. and Verbitsky, I. E.. Radial fractional Laplace operators and Hessian inequalities. J. Differ. Equ. 253 (2012), 244–272.
27Frank, R. L. and Seiringer, R.. Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 255 (2008), 3407–3430.
28Grenon, N., Murat, F. and Porretta, A.. Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. C. R. Math. Acad. Sci. Paris 342 (2006), 23–28.
29Jeanjean, L. and Sirakov, B.. Existence and multiplicity for elliptic problems with quadratic growth in the gradient. Commun. Partial Differ. Equ. 38 (2013), 244–264.
30Kardar, M., Parisi, G. and Zhang, Y.-C.. Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56 (1986), 889–892.
31Kuusi, T., Mingione, G. and Sire, Y.. Nonlocal equations with measure data. Commun. Math. Phys. 337 (2015), 1317–1368.
32Kuusi, T., Mingione, G. and Sire, Y.. Nonlocal self-improving properties. Anal. PDE 8 (2015), 57–114.
33Laskin, N.. Fractional quantum mechanics and lévy path integrals. Phys. Lett. A 268 (2000), 298–305.
34Leonori, T., Peral, I., Primo, A. and Soria, F.. Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations. Discrete Contin. Dyn. Syst. 35 (2015), 6031–6068.
35Millot, V. and Sire, Y.. On a fractional Ginzburg–Landau equation and 1/2-harmonic maps into spheres. Arch. Ration. Mech. Anal. 215 (2015), 125–210.
36Phuc, N. C.. Morrey global bounds and quasilinear Riccati type equations below the natural exponent. J. Math. Pure Appl. 102 (2014), 99–123.
37Ponce, A. C., Elliptic PDEs, measures and capacities. From the Poisson equations to nonlinear Thomas-Fermi problems. EMS Tracts in Mathematics, vol. 23 (Zürich: European Mathematical Society (EMS), 2016).
38Schikorra, A.. Integro-differential harmonic maps into spheres. Commun. Partial Differ. Equ. 40 (2015), 506–539.
39Shieh, T.-T. and Spector, D.. On a new class of fractional partial differential equations. Adv. Calc. Var. 8 (2015), 321–336.
40Sirakov, B.. Solvability of uniformly elliptic fully nonlinear PDE. Arch. Ration. Mech. Anal. 195 (2010), 579–607.
41Stein, E. M., Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 (Princeton, NJ: Princeton University Press, 1970).
42Toland, J. F.. The Peierls–Nabarro and Benjamin–Ono equations. J. Funct. Anal. 145 (1997), 136–150.