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nonlinear parabolic system; fractional differentiability; spatial derivative; weak solution

References:

[1] Amato, R.: **Local differentiability for the solutions to basic systems of higher order**. Matematiche 42 (1987), 109-119. MR 1030910 | Zbl 0693.35025

[2] Campanato, S.: **Elliptic Systems in Divergence Form. Interior Regularity**. Quaderni, Scuola Normale Superiore, Pisa (1980), Italian. MR 0668196

[3] Campanato, S.: **Sulla regolarità delle soluzioni di equazioni differenzialli di tipo ellittico**. Editrice Tecnico Scientifica, Pisa (1963), Italian.

[4] Fattorusso, L.: **A result of differentiability of nonlinear parabolic systems under monotonicity hypothesis**. Rend. Circ. Mat. Palermo, II. Ser. 39 (1990), 412-426 Italian. English summary. MR 1119738 | Zbl 0733.35026

[5] Fattorusso, L.: **Differentiability of solutions of nonlinear second order parabolic systems with quadratic behaviour**. Boll. Unione Mat. Ital., VII. Ser. B 1 (1987), 741-764 Italian. English summary. MR 0916291 | Zbl 0656.35061

[6] Fattorusso, L.: **New contributions to the differentiability of weak solutions of nonlinear parabolic systems of order $2m$ with quadratic growth**. Matematiche 41 (1986), 183-203 Italian. English summary. MR 0998696 | Zbl 0692.35024

[7] Fattorusso, L.: **On the differentiability of weak solutions of nonlinear second order parabolic equations with quadratic growth**. Matematiche 40 (1985), 199-215 Italian. English summary. MR 0959879 | Zbl 0668.35045

[8] Fattorusso, L., Marino, M.: **Local differentiability of nonlinear parabolic systems of second order with nonlinearity $q\geq 2$**. Ric. Mat. 41 (1992), 89-112 Italian. English summary. MR 1305346

[9] Marino, M., Maugeri, A.: **Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth**. Rend. Semin. Mat. Univ. Padova 76 (1986), 219-245. MR 0881572 | Zbl 0622.35030

[10] Naumann, J.: **On the interior differentiability of weak solutions of parabolic systems with quadratic growth nonlinearities**. Rend. Semin. Mat. Univ. Padova 83 (1990), 55-70. MR 1066428 | Zbl 0823.35027