Regularity of the m-symphonic map

Chen, Y., Hong, M.-C., Hungerbühler, N.: Heat flow of $$p$$-harmonic maps with values into spheres. Math. Z. 215, 25–35 (1994)

Coifman, R., Lions, P.L., Meyer, Y., Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl. 72, 247–286 (1993)

Eells, J., Lemaire, L.: A report on harmonic maps. Bull. Lond. Math. Soc. 10, 1–68 (1978)

Eells, J., Lemaire, L.: Another report on harmonic maps. Bull. Lond. Math. Soc. 20, 385–524 (1988)

Evans, L.C.: Partial regularity for stationary harmonic maps into spheres, Arch. Ration. Mech. Anal. 20, 385–524 (1988)

Evans, L.C.: Weak convergence methods of nonlinear partial differential equations. CBMS Regional Conference Series in Mathematics, 74. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (1990)

Fefferman, C., Stein, E.M.: $$H^{p}$$ spaces of several variables. Acta Math. 192(3–4), 137–193 (1972)

Fuchs, M.: The blow-up of $$p$$-harmonic maps. Manuscr. math. 81, 89–94 (1993)

Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Birkhäuser Verlag, Basel (1993)

Giusti, E.: Direct Methods in the Calculus of Variations. World Scientific Publishing Co., London (2003)

Goldstein, P., Strzelecki, P., Zatorska-Goldstein, A.: On polyharmonic maps into spheres in the critical dimension. Ann. Inst. H. Poincaré Anal. Non. Linéaire 26, 1387–1405 (2009)

Hélein, F.: Harmonic maps, conservation laws and moving frames, Cambridge Tracs in Mathematics, vol. 150. Cambridge University Press, Cambridge (2002)

Hildebrandt, S., Widman, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142, 67–86 (1975)

Iwaniec, T., Martin, G.: Geometric function theory and non-linear analysis, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, (2001). Zbl 1045.30011 MR 1859913

Kawai, S., Nakauchi, N.: Some results for stationary maps of a functional related to pullback metrics. Nonlinear Anal. 74, 2284–2295 (2011)

Leone, C., Misawa, M., Verde, A.: A global existence result for the heat flow of higher dimensional H-systems. J. Math. Pures Appl. 97(3), 282–294 (2012)

Misawa, M., Nakauchi, N.: A Hölder continuity of minimizing symphonic maps. Nonlinear Anal. 75, 5971–5974 (2012)

Misawa, M., Nakauchi, N.: A Hölder continuity of symphonic maps into the spheres. Calc. Var. PDE 55, 1–20 (2016)

Morrey, C.B.: Multiple Integrals in the Calculus of Variations. Springer, Berlin (1966)

Nakauchi, N.: A variational problem related to conformal maps. Osaka J. Math. 48, 717–739 (2011)

Nakauchi, N., Takenaka, Y.: A variational problem for pullback metrics. Ricerche di Mat. 60, 219–235 (2011)

Riviére, T., Strzelecki, P.: A sharp nonlinear Gagliardo-Nirenberg-type estimates and applications to the regularity of elliptic systems. Comm. Partial Differ. Equ. 30(4–6), 589–604 (2005)

Schikorra, A., Strzelecki, P.: Invitation to H-systems in higher dimensions: known results, new facts, and related open problems. EMS Surv. Math. Sci. 4(1), 21–42 (2017)

Stein, E.M.: Harmonic Analysis, Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton (1993)

Strzelecki, P.: Regularity of p-harmonic maps from p-dimensional ball into a sphere. Manuscr. Math. 82(3–4), 407–415 (1994)

Strzelecki, P., Zatorska-Goldstein, A.: A compactness theorem for weak solutions of higher-dimensional H-systems. Duke Math. J. 121(2), 269–284 (2004)

Takeuchi, H.: Some conformal properties of p-harmonic maps and a regularity for sphere-valued p-harmonic maps. J. Math. Soc. Jpn. 46(2), 217–234 (1994)

Torchinsky, A.: Real Variable Methods in Harmonic Analysis. Academic Press, New York (1986)

Widman, K.-O.: Hölder continuity of solutions of elliptic systems. Manuscr. Math. 5, 299–308 (1971)

Zeidler, E.: Nonlinear Functional Analysis and its Applications II / B (Nonlinear Monotonic operators). Springer, New York (1990)