The Experts below are selected from a list of 25206 Experts worldwide ranked by ideXlab platform
Vicenţiu D Rădulescu - One of the best experts on this subject based on the ideXlab platform.
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on a new fractional Sobolev Space and applications to nonlocal variational problems with variable exponent
Discrete and Continuous Dynamical Systems - Series S, 2017Co-Authors: Anouar Bahrouni, Vicenţiu D RădulescuAbstract:The content of this paper is at the interplay between function Spaces $L^{p(x)}$ and $W^{k, p(x)}$ with variable exponents and fractional Sobolev Spaces $W^{s, p}$. We are concerned with some qualitative properties of the fractional Sobolev Space $W^{s, q(x), p(x, y)}$, where $q$ and $p$ are variable exponents and $s∈ (0, 1)$. We also study a related nonlocal operator, which is a fractional version of the nonhomogeneous $p(x)$-Laplace operator. The abstract results established in this paper are applied in the variational analysis of a class of nonlocal fractional problems with several variable exponents.
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two non trivial solutions for a non homogeneous neumann problem an orlicz Sobolev Space setting
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2009Co-Authors: Alexandru Kristaly, Mihai Mihăilescu, Vicenţiu D RădulescuAbstract:In this paper we study a non-homogeneous Neumann-type problem which involves a nonlinearity satisfying a non-standard growth condition. By using a recent variational principle of Ricceri, we establish the existence of at least two non-trivial solutions in an appropriate Orlicz–Sobolev Space.
Ye Peixin - One of the best experts on this subject based on the ideXlab platform.
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probabilistic and average linear widths of Sobolev Space with gaussian measure in l norm
Constructive Approximation, 2003Co-Authors: Fang Gensun, Ye PeixinAbstract:In this paper we investigate the probabilistic linear $(n,\delta)$-widths and $p$-average linear $n$-widths of the Sobolev Space $W^r_2$ equipped with the Gaussian measure $\mu$ in the $L_{\infty}$-norm, and determine the asymptotic equalities \begin{eqnarray*} \lambda_{n,\delta}(W^r_2,\mu,L_{\infty}) &\asymp&\frac{\sqrt{\ln (n/\delta)}}{n^{r+(s-1)/2}},\\[3pt] \lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty. \end{eqnarray*}
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probabilistic and average linear widths of Sobolev Space with gaussian measure
Journal of Complexity, 2003Co-Authors: Fang Gensun, Ye PeixinAbstract:We determine the exact order of the p-average linear n-widths λn(a) (W2r, µ, Lq)p, 1 ≤ q > ∞, 0 > p > ∞, of the Sobolev Space W2r equipped with a Gaussian measure µ in the Lq-norm.Moreover, we also calculate the probabilistic linear (n, δ)-widths and p-average linear n- widths of the finite-dimensional Space Rm with the standard Gaussian measure in lqm, i.e., λn,δ(Rm, vm, lqm)~m1/q-1/2 √m + ln(1/δ), 1 ≤ q > 2, m ≥ 2n, δ ∈ (0, 1/2], λn(a) (Rm, vm, lqm)p~m1/q, 1 ≤ q > ∞, 0 > p > ∞, m ≥ 2n, δ ∈ (0, 1/2]. For the case of 2 ≤ q ≤ ∞, Maiorov and Wasilkowski have obtained the exact order of the probabilistic linear (n, δ)-widths λn,δ(Rm, vm, lqm), 2 ≤ q ≤ ∞, and p-average linear n-widths λn(a) (Rm, vm, lqm)1,q = ∞, p = 1.
Fang Gensun - One of the best experts on this subject based on the ideXlab platform.
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probabilistic and average linear widths of Sobolev Space with gaussian measure in l norm
Constructive Approximation, 2003Co-Authors: Fang Gensun, Ye PeixinAbstract:In this paper we investigate the probabilistic linear $(n,\delta)$-widths and $p$-average linear $n$-widths of the Sobolev Space $W^r_2$ equipped with the Gaussian measure $\mu$ in the $L_{\infty}$-norm, and determine the asymptotic equalities \begin{eqnarray*} \lambda_{n,\delta}(W^r_2,\mu,L_{\infty}) &\asymp&\frac{\sqrt{\ln (n/\delta)}}{n^{r+(s-1)/2}},\\[3pt] \lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty. \end{eqnarray*}
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probabilistic and average linear widths of Sobolev Space with gaussian measure
Journal of Complexity, 2003Co-Authors: Fang Gensun, Ye PeixinAbstract:We determine the exact order of the p-average linear n-widths λn(a) (W2r, µ, Lq)p, 1 ≤ q > ∞, 0 > p > ∞, of the Sobolev Space W2r equipped with a Gaussian measure µ in the Lq-norm.Moreover, we also calculate the probabilistic linear (n, δ)-widths and p-average linear n- widths of the finite-dimensional Space Rm with the standard Gaussian measure in lqm, i.e., λn,δ(Rm, vm, lqm)~m1/q-1/2 √m + ln(1/δ), 1 ≤ q > 2, m ≥ 2n, δ ∈ (0, 1/2], λn(a) (Rm, vm, lqm)p~m1/q, 1 ≤ q > ∞, 0 > p > ∞, m ≥ 2n, δ ∈ (0, 1/2]. For the case of 2 ≤ q ≤ ∞, Maiorov and Wasilkowski have obtained the exact order of the probabilistic linear (n, δ)-widths λn,δ(Rm, vm, lqm), 2 ≤ q ≤ ∞, and p-average linear n-widths λn(a) (Rm, vm, lqm)1,q = ∞, p = 1.
Duchao Liu - One of the best experts on this subject based on the ideXlab platform.
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on a compact trace embedding theorem in musielak Sobolev Spaces
arXiv: Functional Analysis, 2019Co-Authors: Li Wang, Duchao LiuAbstract:By a stronger compact boundary embedding theorem in Musielak-Orlicz-Sobolev Space developed in the paper, variational method is employed to deal with the nonlinear elliptic equation with the nonlinear Neumann boundary condition in the framework of Musielak-Orlicz-Sobolev Space.
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holder continuity for nonlinear elliptic problem in musielak orlicz Sobolev Space
Journal of Differential Equations, 2019Co-Authors: Beibei Wang, Duchao Liu, Peihao ZhaoAbstract:Abstract Under appropriate assumptions on the N ( Ω ) -function, the De Giorgi process is presented by the tools recently developed in Musielak–Orlicz–Sobolev Space to prove the Holder continuity of fully nonlinear elliptic problems. As the applications, the Holder continuity of the minimizers for a class of the energy functionals in Musielak–Orlicz–Sobolev Spaces is proved; and furthermore, the local Holder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided.
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h o lder continuity for nonlinear elliptic problem in musielak orlicz Sobolev Space
arXiv: Analysis of PDEs, 2017Co-Authors: Beibei Wang, Duchao Liu, Peihao ZhaoAbstract:Under appropriate assumptions on the $N(\Omega)$-fucntion, the De Giorgi process is presented in the framework of Musielak-Orlicz-Sobolev Space to prove the H\"{o}lder continuity of fully nonlinear elliptic problems. As the applications, the H\"{o}lder continuity of the minimizers for a class of the energy functionals in Musielak-Orlicz-Sobolev Spaces is proved; and furthermore, the H\"{o}lder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided.
Ahmad Javid - One of the best experts on this subject based on the ideXlab platform.
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a study on single iteration Sobolev descent for linear initial value problems
Optical and Quantum Electronics, 2021Co-Authors: Sultan Sial, Aly R Seadawy, Nauman Raza, Adnan Khan, Ahmad JavidAbstract:Mahavier and Montgomery construct a Sobolev Space for approximate solution of linear initial value problems in a finite difference setting in single-iteration Sobolev descent for linear initial value problems, Mahavier, Montgomery, MJMS, 2013. Their Sobolev Space is constructed so that gradient-descent converges to a solution in a single iteration, demonstrating the existence of a best Sobolev gradient for finite difference approximation of solutions of linear initial value problems. They then ask if there is a broader class of problems for which convergence in a single iteration in an appropriate Sobolev Space occurs. We use their results to show the existence of single-step iteration to solution in a lower dimensional Sobolev Space for their examples and then a class of problems for single-step convergence.
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a note on single iteration Sobolev descent for linear initial value problems
Authorea Preprints, 2020Co-Authors: Sultan Sial, Nauman Raza, Adnan Khan, Ahmad JavidAbstract:Mahavier and Montgomery construct a Sobolev Space for approximate solution of linear initial value problems in a finite difference setting in SINGLE-ITERATION Sobolev DESCENT FOR LINEAR INITIAL VALUE PROBLEMS, Mahavier, Montgomery, MJMS, 2013. Their Sobolev Space is constructed so that gradient-descent converges to a solution in a single iteration, demonstrating the existence of a best Sobolev gradient for finite difference approximation of solutions of linear initial value problems. They then ask if there is a broader class of problems for which convergence in a single iteration in an appropriate Sobolev Space occurs. We use their results to show the existence of single-step iteration to solution in a lower dimensional Sobolev Space for their examples and then a class of problems for single-step convergence.
