Geodesic
Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. Solvability and regularity problems
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 18-31

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We consider nondiagonal elliptic and parabolic systems of equations with strongly nonlinear terms in the gradient. We review and comment known solvability and regularity results and describe the last author's results in this field.
Keywords: nonlinear elliptic systems, nonlinear parabolic systems, regularity of weak solutions. 
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     author = {A. A. Arkhipova},
     title = {Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. {Solvability} and regularity problems},
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A. A. Arkhipova. Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. Solvability and regularity problems. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 18-31. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a1/