Existence and uniqueness results for Dirichlet problem in weighted Sobolev spaces on unbounded domains

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Existence and Uniqueness of Solution for P-Laplacian Dirichlet Problem

whereΔp is the p-Laplacian, Ω ∈ C0,1 be a bounded domain inRN . Let p ≥ 2, λ > 0 and f : Ω×R −→ R be a caratheodory function which is decreasing with respect to the second variable, i.e., f(x, s1) ≥ f(x, s2) for a.a. x ∈ Ω ands1, s2 ∈ R, s1 ≤ s2 (2) Assume, moreover, that there exists f0 ∈ Lp(Ω), p′ = p p−1 and c > 0 such that ∣f(x, s)∣ ≤ f0(x) + c∣s∣p−1 (3) We considered such problems with num...

Weighted Sobolev spaces and regularity for polyhedral domains

We prove a regularity result for the Poisson problem −∆u = f , u|∂P = g on a polyhedral domain P ⊂ R 3 using the Babuška–Kondratiev spaces Ka (P). These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4, 29]. In particular, we show that there is no loss of Ka –regularity for solutions of strongly elliptic systems with smooth coefficients. We also es...