Optimization Problem for Extremals of the Trace Inequality in Domains with Holes
نویسنده
چکیده
Let Ω be a bounded smooth domain in R with N ≥ 2 and 1 < p < ∞. We denote by p∗ the critical exponent for the Sobolev trace immersion given by p∗ = p(N − 1)/(N − p) if p < N and p∗ = ∞ if p ≥ N . For any A ⊂ Ω, which is a smooth open subset, we define the space W 1,p A (Ω) = C ∞ 0 (Ω \A), where the closure is taken in W −norm. By the Sobolev Trace Theorem, there is a compact embedding (1.1) W 1,p A (Ω) →֒ L (∂Ω), for all 1 < q < p. Thus, given 1 < q < p, there exist a constant C = C(q, p) such that
منابع مشابه
An Optimization Problem Related to the Best Sobolev Trace Constant in Thin Domains
Let Ω ⊂ RN be a bounded, smooth domain. We deal with the best constant of the Sobolev trace embedding W 1,p(Ω) ↪→ Lq(∂Ω) for functions that vanish in a subset 17 A ⊂ Ω, which we call the hole, i.e. we deal with the minimization problem SA = inf ‖u‖ W1,p(Ω) /‖u‖ Lq(∂Ω) for functions that verify u |A = 0. It is known that there 19 exists an optimal hole that minimizes the best constant SA among s...
متن کاملSequential Optimality Conditions and Variational Inequalities
In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...
متن کاملFekete-Szegö Problem of Functions Associated with Hyperbolic Domains
In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...
متن کاملThe Best Constant and Extremals of the Sobolev Embeddings in Domains with Holes: the L∞ Case
Let Ω ⊂ R be a bounded, convex domain. We study the best constant of the Sobolev trace embedding W 1,∞(Ω) ↪→ L∞(∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole. That is, we deal with the minimization problem S A = inf ‖u‖W1,∞(Ω)/‖u‖L∞(∂Ω) for functions that verify u |A= 0. We find that there exists an optimal hole that minimizes the best constant S A among subsets of Ω o...
متن کاملLinear optimization on Hamacher-fuzzy relational inequalities
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Hamacher family of t-norms is considered as fuzzy composition. Hamacher family of t-norms is a parametric family of continuous strict t-norms, whose members are decreasing functions of ...
متن کامل