Abstract
The Hopf’s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form (g(u)u, i ), i +f(x, u, q) = 0 (q = |∇u|2), subject to Dirichlet, Neumann or Robin boundary conditions. The principles derived may be used to deduce bounds on the gradient q.
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Supported by the National Natural Science Foundation of China (No.60174007) and PNSFS.
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Ding, Jt., Li, Sj. & Hao, Jh. Maximum Principles for a Class of Nonlinear Elliptic Boundary Value Problems. Acta Mathematicae Applicatae Sinica, English Series 21, 373–380 (2005). https://doi.org/10.1007/s10255-005-0244-9
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DOI: https://doi.org/10.1007/s10255-005-0244-9