PHYSICS AND MATHEMATICS

Estimates for the solution in $C^0(S_1^2)$ metric of a quasilinear equation of general form

T. A. Yuryeva, N. A. Chalkina

Amur State University

Abstract: The questions of the existence and uniqueness of regular surfaces with the given geometric characteristics in one or another space are analytically equivalent to considering and investigating the unique solvability of partial differential equations on one or another manifold. The paper provides a proof that a priori estimates for the solution of a generalized quasilinear equation on the unit sphere $S_1^2$ exist. It also considers special cases of a generalized quasilinear equation related to geometric problems.

Keywords: quasilinear equation, positive ellipticity, a priori estimates, quadratic form.

DOI: 10.23670/IRJ.2020.100.10.004