Phragmén–Lindelöf theorems for a weakly elliptic equation with a nonlinear dynamical boundary condition

A Spectral Method for an Elliptic Equation with a Nonlinear Neumann Boundary Condition

Abstract. Let Ω be an open, simply connected, and bounded region in Rd, d ≥ 2, that is diffeomorphic to Bd. Consider solving −∆u+ γu = 0 over Ω with the Neumann boundary condition ∂u ∂n = b (·, u). The function b is a nonlinear function of u. The problem is reformulated in a weak form, and then a spectral Galerkin method is used to create a sequence of finite dimensional nonlinear problems. An ...

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Abstract. We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition −∂u/∂νA = g(·, ·, u) with a locally defined, Lr-bounded function g(t, ·, ξ). We prove the existence of a local weak solution to the problem by means of ...

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...