We consider the nonlinear Neumann problem for fully elliptic PDEs on a quadrant. establish comparison theorem viscosity sub- and supersolutions of problem. The crucial argument in proof is to build $C^{1,1}$ test function which takes care boundary condition. A similar has been treated general $n$-dimensional orthant by Biswas et al. [SIAM J. Control Optim., 55 (2017), pp. 365--396], where funct...

In this paper we study fully nonlinear obstacle type problems in Hilbert spaces. We introduce the notion of Q-elliptic equation and prove existence, uniqueness, and regularity of viscosity solutions of Q-elliptic obstacle problems. In particular we show that solutions of concave problems with semiconvex obstacles are in the space W 2,∞ Q .

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

For plecewise linear approximation of variational inequalities associated with the mildly nonlinear elliptic boundary value problems having auxiliary constraint conditions, we prove that the error estimate for u-uh in the W 1’2norm is of order h. KEV WORDS AND PHRASES. Fine Element, V)nal Inequalities, Approximation, Mdly nonlinear. 1980 THEMATICS SUBJECT CLASSIFICATION CODES. Primary 5J20, 65N...

We prove that viscosity solutions in W 1'~176 of the second order, fully nonlinear, equation F(D2u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) Fis uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions ont...

Nonlinear elliptic transport systems arise in various problems in applied mathematics, most often leading to large-scale problems owing to the huge number of equations, see e.g. [14, 17, 18]. For large-scale elliptic problems, iterative processes are the most widespread solution methods, which often rely on Hilbert space theory when mesh independence is desired. (See e.g. [7, 11, 12] and the au...