Denoting by S the sharp constant in the Sobolev inequality in W1,2 0 (B), being B the unit ball in ℝ, and denoting by Sh its approximation in a suitable finite element space, we show that Sh converges to S as h south east double arrow 0 with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results
We address fundamental aspects in the approximation theory of vector-valued finite element methods, ...
AbstractWe give a new proof of the following inequality. In any dimensionn≥2 and for 1<p<nlets=(n+p)...
International audienceWe estimate best-approximation errors using vector-valued finite elements for ...
Denoting by S the sharp constant in the Sobolev inequality in W1,2 0 (B), being B the unit ball in ℝ...
Abstract. We consider the finite element method applied to nonlinear Sobolev equation with smooth da...
A numerical method for the computation of the best constant in a Sobolev inequality involving the sp...
AbstractThis work is a continuation of the recent study by the authors on approximation theory over ...
We consider the Sobolev embeddings E1 : W01,p(a,b)→Lp(a,b) and E2 : L1,p(a,b)/{1}→Lp(a,b)/{1}, ...
Abstract: The paper is devoted to the development of Fedorenko finite superelement method ...
AbstractWe consider the Sobolev embeddingsE1:W01,p(a,b)→Lp(a,b)andE2:L1,p(a,b)/{1}→Lp(a,b)/{1},with ...
AbstractWe consider the Sobolev (Bessel potential) spaces Hℓ(Rd,C), and their standard norms ‖ ‖ℓ (w...
We establish upper and lower estimates for the embedding constants related to the classical Sobolev ...
We consider the imbedding inequality || f ||_{L^r} <= S_{r,n,d} || f ||_{H^{n}}; H^{n}(R^d) is the...
Let B1 be the unit ball of R N , N ? 2, and let p ? = N p/(N ? p) if 1 < p < N and p ? = ? if p ?...
In this paper, we construct compactly supported radial basis functions that satisfy optimal approxim...
We address fundamental aspects in the approximation theory of vector-valued finite element methods, ...
AbstractWe give a new proof of the following inequality. In any dimensionn≥2 and for 1<p<nlets=(n+p)...
International audienceWe estimate best-approximation errors using vector-valued finite elements for ...
Denoting by S the sharp constant in the Sobolev inequality in W1,2 0 (B), being B the unit ball in ℝ...
Abstract. We consider the finite element method applied to nonlinear Sobolev equation with smooth da...
A numerical method for the computation of the best constant in a Sobolev inequality involving the sp...
AbstractThis work is a continuation of the recent study by the authors on approximation theory over ...
We consider the Sobolev embeddings E1 : W01,p(a,b)→Lp(a,b) and E2 : L1,p(a,b)/{1}→Lp(a,b)/{1}, ...
Abstract: The paper is devoted to the development of Fedorenko finite superelement method ...
AbstractWe consider the Sobolev embeddingsE1:W01,p(a,b)→Lp(a,b)andE2:L1,p(a,b)/{1}→Lp(a,b)/{1},with ...
AbstractWe consider the Sobolev (Bessel potential) spaces Hℓ(Rd,C), and their standard norms ‖ ‖ℓ (w...
We establish upper and lower estimates for the embedding constants related to the classical Sobolev ...
We consider the imbedding inequality || f ||_{L^r} <= S_{r,n,d} || f ||_{H^{n}}; H^{n}(R^d) is the...
Let B1 be the unit ball of R N , N ? 2, and let p ? = N p/(N ? p) if 1 < p < N and p ? = ? if p ?...
In this paper, we construct compactly supported radial basis functions that satisfy optimal approxim...
We address fundamental aspects in the approximation theory of vector-valued finite element methods, ...
AbstractWe give a new proof of the following inequality. In any dimensionn≥2 and for 1<p<nlets=(n+p)...
International audienceWe estimate best-approximation errors using vector-valued finite elements for ...
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