Partial regularity for a nonlinear discontinuous sub-elliptic system with drift on the Heisenberg group: the superquadratic case

References

• Sarason D. Functions of vanishing mean oscillation. Trans Am Math Soc. 1975;207(1):391–405.
   Google Scholar
• Chiarenza F, Frasca M, Longo P. W2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients. Trans Am Math Soc. 1993;336(2):841–853.
   Web of Science ®Google Scholar
• Lanconelli E, Polidoro S On a class of hypoelliptic evolution operators. Partial differential equations, II (Turin, 1993). Rend. Sem. Mat. Univ. Politec. Torino, 52(1), 1994. p. 29–63.
   Google Scholar
• Lanconelli E, Pascucci A, Polidoro S Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance. Nonlinear problems in mathematical physics and related topics, II. New York: Kluwer/Plenum; 2002. p. 243–265. (Int. Math. Ser. (N. Y.), vol. 2).
   Google Scholar
• Bramanti M An invitation to hypoelliptic operators and Hörmander's vector fields. Cham: Springer; 2014. (Springer briefs in mathematics).
   Google Scholar
• Hörmander L. Hypoelliptic second order differential equations. Acta Math. 1967;119(3):147–171.
   Web of Science ®Google Scholar
• Folland G, Stein E. Estimates for the ∂¯b-complex and analysis on the Heisenberg group. Commun Pure Appl Math. 1974;27(4):429–522.
   Web of Science ®Google Scholar
• Bramanti M, Zhu M. Lp and Schauder estimates for nonvariational operators structured on Hörmander vector fields with drift. Anal PDE. 2013;6(8):1793–1855.
   Web of Science ®Google Scholar
• Kohn J. Pseudo-differential operators and hypoellipticity. Proc Symp Pure Math. 1973;23:61–69.
   Google Scholar
• Austin AD, Tyson JT. A new proof of the C∞ regularity of C2 conformal mappings on the Heisenberg group. Colloq Math. 2017;150(2):217–228.
   Web of Science ®Google Scholar
• Du G, Han J, Niu P. Interior regularity for degenerate equations with drift on homogeneous groups. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM. 2019;113(2):587–604.
   Web of Science ®Google Scholar
• Feng X, Niu P. Interior regularity for degenerate elliptic equations with drift on homogeneous groups. J Lie Theory. 2013;23(3):803–825.
   Web of Science ®Google Scholar
• Hou Y, Feng X, Cui X. Global Hölder estimates for hypoelliptic operators with drift on homogeneous groups. Miskolc Math Notes. 2012;13(2):337–347.
   Web of Science ®Google Scholar
• Hou Y, Niu P. Weighted Sobolev–Morrey estimates for hypoelliptic operators with drift on homogeneous groups. J Math Anal Appl. 2015;428(2):1319–1338.
   Web of Science ®Google Scholar
• Zhang J, Wang J. Regularity for a nonlinear discontinuous subelliptic system with drift on the Heisenberg group. Adv Math Phys. 2022;2022:14.
   Web of Science ®Google Scholar
• Zhang J, Niu P. C1,α-Regularity for quasilinear degenerate elliptic equation with a drift term on the Heisenberg group. Bull Sci Math. 2022;175(2):103097.
   Google Scholar
• Wang J, Manfredi JJ. Partial Hölder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group. Adv Nonlinear Anal. 2018;7(1):96–114.
   Web of Science ®Google Scholar
• Duzaar F, Steffen K. Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals. J Reine Angew Math. 2002;546(5):73–138.
   Google Scholar
• Duzaar F, Grotowski JF. Partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation. Manuscripta Math. 2000;103(3):267–298.
   Web of Science ®Google Scholar
• Duzaar F, Mingione G. The p-harmonic approximation and the regularity of p-harmonic maps. Calc Var Partial Differ Equ. 2004;20(3):235–256.
   Web of Science ®Google Scholar
• Duzaar F, Mingione G. Regularity for degenerate elliptic problems via p-harmonic approximation. Ann Inst H Poincaré Anal Non Linèaire. 2004;21(5):735–766.
   Web of Science ®Google Scholar
• Tan Z, Wang Y. Partial regularity for subquadratic homogeneity elliptic system with VMO-coefficients. J Math Anal Appl. 2017;454(2):617–638.
   Web of Science ®Google Scholar
• Tan Z, Wang Y, Chen S. Partial regularity in the interior for discontinuous inhomogeneous elliptic system with VMO-coefficients. Ann Mat Pura Appl. 2017;196(4):85–105.
   Google Scholar
• Tan Z, Wang Y, Chen S. Partial regularity up to the boundary for solutions of subquadratic elliptic systems. Adv Nonlinear Anal. 2018;7(4):469–483.
   Web of Science ®Google Scholar
• Wang J, Liao Q, Zhu M, et al. Partial regularity for discontinuous sub-elliptic systems with VMO-coefficients involving controllable growth terms in Heisenberg groups. Nonlinear Anal. 2019;178(1):227–246.
   Google Scholar
• Wang J, Zhu M, Gao S, et al. Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case. Adv Nonlinear Anal. 2021;10(1):420–449.
   Web of Science ®Google Scholar
• Folland G, Stein E Hardy spaces on homogeneous group. Princeton (NJ): Princeton University Press; 1982. (Mathematical notes, no. 28).
   Google Scholar
• Capogna L. Regularity of quasi-linear equations in the Heisenberg group. Commun Pure Appl Math. 1997;50(9):867–889.
   Web of Science ®Google Scholar
• Bonfiglioli A, Lanconelli E, Uguzzoni F Stratified Lie groups and potential theory for their sub-Laplacians. Berlin: Springer; 2007. (Springer monographs in mathematics).
   Google Scholar
• Capogna L, Danielli D, Garofalo N. An embedding theorem and Harnack inequality for nonlinear subelliptic equations. Commun Partial Differ Equ. 1993;18(9-10):1765–1794.
   Web of Science ®Google Scholar
• Zhang J, Niu P. Hölder regularity of quasiminimizers to generalized Orlicz functional on the Heisenberg group. J Funct Spaces. 2020;2020:13.
   Web of Science ®Google Scholar
• Föglein A. Partial regularity results for sub-elliptic systems in the Heisenberg group. Calc Var Partial Differ Equ. 2008;32(1):25–51.
   Web of Science ®Google Scholar
• Ding Y. Foundation of modern analysis. Beijing: Beijing Normal University Press; 2008 (in Chinese).
   Google Scholar