Abstract
This paper mainly concerns oblique derivative problems for nonlinear nondivergent elliptic equations of second order with measurable coefficients in a multiply connected domain. Under certain condition, we derive a priori estimates of solutions. By using these estimates and the fixed-point theorem, we prove the existence of solutions.
Highlights
The above equation can be rewritten in the form x, u, Dxu, Dx2u
The main equation to be studied in this paper is
Where k0, i i 0,1, N are positive constants, we say that the Equation (1.2) satisfies Condition C
Summary
Dx2u, continuous in u , Dxu N. where k0, i i 0,1, , N are positive constants, we say that the Equation (1.2) satisfies Condition C. It is enough to consider the linear elliptic Equation of (1.1), namely aij i, j 1 x uxi x j bi i 1 x uxi c x u. Where aij ,bi ,c are as stated in (1.2) Multiplying both sides of (1.1) by u we obtain the following equation on u2 :. 2. Estimates of Solutions of Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order. Any solution u x of Problem O satisfies the estimates. After substituting the solution u x into (1.2), we see that we only need to discuss the linear elliptic equation in the form (2.3). Are non-negative constants, k* k1 k2 k3 with k1 in (1.5), k2 in (1.9), and k3
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