All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 72 Next

Displaying 1421 – 1440 of 5493

Showing per page

Estimates of solutions to linear elliptic systems and equations

Heinrich Begehr (1992)

Banach Center Publications

Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in ℝ m . Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic...

Estimates of the principal eigenvalue of the p -Laplacian and the p -biharmonic operator

Jiří Benedikt (2015)

Mathematica Bohemica

We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet p -Laplacian and the Navier p -biharmonic operator on a ball of radius R in ℝ N and its asymptotics for p approaching 1 and ∞ . Let p tend to ∞ . There is a critical radius R C of the ball such that the principal eigenvalue goes to ∞ for 0 < R ≤ R C and to 0 for R > R C . The critical radius is R C = 1 for any N ∈ ℕ for the p -Laplacian and R C = 2 N in the case of the p -biharmonic operator. When p approaches 1 , the principal eigenvalue of the Dirichlet...

Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert, Luis Silvestre (2016)

Journal of the European Mathematical Society

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Estimates on the solution of an elliptic equation related to Brownian motion with drift (II).

Joseph G. Conlon, Peder A. Olsen (1997)

Revista Matemática Iberoamericana

In this paper we continue the study of the Dirichlet problem for an elliptic equation on a domain in R3 which was begun in [5]. For R &gt; 0 let ΩR be the ball of radius R centered at the origin with boundary ∂Ω R. The Dirichlet problem we are concerned with is the following:(-Δ - b(x).∇) u(x) = f(x),   x ∈ Ω R,with zero boundary conditionsu(x) = 0,   x ∈ ∂Ω R.

Estimates on the solution of an elliptic equation related to Brownian motion with drift.

Joseph G. Conlon, Juan Redondo (1995)

Revista Matemática Iberoamericana

In this paper we are concerned with studying the Dirichlet problem for an elliptic equation on a domain in R3. For simplicity we shall assume that the domain is a ball ΩR of radius R. Thus:ΩR = {x ∈ R3 : |x| &lt; R}.The equation we are concerned with is given by(-Δ - b(x).∇) u(x) = f(x),    x ∈ ΩR,with zero Dirichlet boundary conditions.

Currently displaying 1421 – 1440 of 5493