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Search Results: 1 - 10 of 1320 matches for " orlicz-sobolev spaces "
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PERIODIC SOLUTIONS IN THE SINGULAR LOGARITHMIC POTENTIAL
VIDAL,CLAUDIO;
Proyecciones (Antofagasta) , 2007, DOI: 10.4067/S0716-09172007000200003
Abstract: we consider the singular logarithmic potential , a potential which plays an important role in the modelling of triaxial systems, such as elliptical galaxies or bars in the centres of galaxy discs. using properties of the central field in the axis-symmetric case we obtain periodic solutions which are symmetric with respect to the origin for weak anisotropies. also we generalize our result in order to include more general perturbations of the logarithmic potential.
PERIODIC SOLUTIONS IN THE SINGULAR LOGARITHMIC POTENTIAL
CLAUDIO VIDAL
Proyecciones (Antofagasta) , 2007,
Abstract: We consider the singular logarithmic potential , a potential which plays an important role in the modelling of triaxial systems, such as elliptical galaxies or bars in the centres of galaxy discs. Using properties of the central field in the axis-symmetric case we obtain periodic solutions which are symmetric with respect to the origin for weak anisotropies. Also we generalize our result in order to include more general perturbations of the logarithmic potential.
Strongly nonlinear parabolic initial-boundary value problems in Orlicz spaces
Abdelhak Elmahi
Electronic Journal of Differential Equations , 2002,
Abstract: problems. We also prove some compactness results in inhomogeneous Orlicz-Sobolev spaces.
Orlicz-Sobolev空间的端点与严格凸性
The Extreme Points and Rotundity of Orlicz-Sobolev Spaces
 [PDF]

曹法赟
Pure Mathematics (PM) , 2015, DOI: 10.12677/PM.2015.53018
Abstract:
本文在Orlicz-Sobolev空间上给出了一种模范数,给出了由严格凸N函数生成Orlicz-Sobolev空间严格凸的充要条件。
In this paper we give a modular norm for Orlicz-Sobolev spaces, and obtain a necessary and suffi-cient condition for the Orlicz-Sobolev spaces which is formed by strictly convex N function to be rotund.
Variational inequalities for energy functionals with nonstandard growth conditions
Martin Fuchs,Li Gongbao
Abstract and Applied Analysis , 1998, DOI: 10.1155/s1085337598000438
Abstract:
Elliptic equations with measure data in Orlicz spaces
Ge Dong
Electronic Journal of Differential Equations , 2008,
Abstract: This article shows the existence of solutions to the nonlinear elliptic problem $A(u)=f$ in Orlicz-Sobolev spaces with a measure valued right-hand side, where $A(u)=-mathop{ m div}a(x,u, abla u)$ is a Leray-Lions operator defined on a subset of $W_{0}^{1}L_{M}(Omega)$, with general $M$.
Orlicz-Sobolev空间上对称及非对称拟线性椭圆方程的多解性
MULTIPLE SOLUTIONS FOR SYMMETRIC AND NON-SYMMETRIC QUASILINEAR ELLIPTIC EQUATIONS:AN ORLICZ-SOBOLEV SPACE SETTING

作者,杨阳,张吉慧,尚旭东,邵益新
- , 2015,
Abstract: 本文研究了具光滑边界的有界域上拟线性椭圆问题的多解性.在Orlicz-Sobolev空间中利用变分及扰动的方法,得到了方程在对称及非对称情况下解的存在性和多解性.
In this paper,we study multiplicity of solutions for the quasilinear elliptic problem in a bounded domain with smooth boundary.By using variational and perturbed methods in Orlicz-Sobolev space,we prove the existence of multiple solutions both in symmetric and nonsymmetric case
WEAK CONVERGENCE OF JACOBIAN DETERMINANTS Weak convergence of Jacobian determinants under asymmetric assumptions
Teresa Alberico,Costantino Capozzoli
Le Matematiche , 2012,
Abstract: Let $Om$ be a bounded open set in $R^2$ sufficiently smooth and $f_k=(u_k,v_k)$ and $f=(u,v)$ mappings belong to the Sobolev space $W^{1,2}(Omega, R^2)$. We prove that if the sequence of Jacobians $J_{f_k}$ converges to a measure $mu$ in sense of measures and if one allows different assumptions on the two components of $f_k$ and $f$, e.g. $$ u_k ightharpoonup u ;;mbox{weakly in} ;; W^{1,2}(Omega) qquad , v_k ightharpoonup v ;;mbox{weakly in} ;; W^{1,q}(Omega) $$ for some $qin(1,2)$, then egin{equation}label{0} dmu=J_f,dz. end{equation} Moreover, we show that this result is optimal in the sense that conclusion fails for $q=1$. On the other hand, we prove that eqref{0} remains valid also if one considers the case $q=1$, but it is necessary to require that $u_k$ weakly converges to $u$ in a Zygmund-Sobolev space with a slightly higher degree of regularity than $W^{1,2}(Omega)$ and precisely $$ u_k ightharpoonup u ;;mbox{weakly in} ;; W^{1,L^2 log^alpha L}(Omega)$$ for some $alpha > 1$. Let $Om$ be a bounded open set in $R^2$ sufficiently smooth and $f_k=(u_k,v_k)$ and $f=(u,v)$ mappings belong to the Sobolev space $W^{1,2}(Om,R^2)$. We prove that if the sequence of Jacobians $J_{f_k}$ converges to a measure $mu$ in sense of measures and if one allows different assumptions on the two components of $f_k$ and $f$, e.g. $$ u_k ightharpoonup u ;;mbox{weakly in} ;; W^{1,2}(Om) qquad , v_k ightharpoonup v ;;mbox{weakly in} ;; W^{1,q}(Om) $$ for some $qin(1,2)$, then egin{equation}label{0} dmu=J_f,dz. end{equation} Moreover, we show that this result is optimal in the sense that conclusion fails for $q=1$. On the other hand, we prove that eqref{0} remains valid also if one considers the case $q=1$, but it is necessary to require that $u_k$ weakly converges to $u$ in a Zygmund-Sobolev space with a slightly higher degree of regularity than $W^{1,2}(Om)$ and precisely $$ u_k ightharpoonup u ;;mbox{weakly in} ;; W^{1,L^2 log^alpha L}(Om)$$ for some $alpha >1$.
Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces
Ahmed Youssfi
Electronic Journal of Differential Equations , 2007,
Abstract: We prove the existence of bounded solutions for the nonlinear elliptic problem$$ -mathop{m div}a(x,u,{ abla}u)=f quad ext{in }{Omega},$$ with $uin W^1_0L_M({Omega})cap L^{infty}(Omega)$, where$$ a(x,s,xi)cdotxigeq {overline M}^{-1}M(h(|s|))M(|xi|),$$ and $h:{mathbb{R}^+}{ o }{]0,1]}$ is a continuous monotone decreasing function with unbounded primitive. As regards the $N$-function $M$, no $Delta_2$-condition is needed.
Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces
George Dinca,Pavel Matei
Electronic Journal of Differential Equations , 2007,
Abstract: Let $a:mathbb{R} o mathbb{R}$ be a strictly increasing odd continuous function with $lim_{t o +infty }a(t)=+infty $ and $A(t)=int_{0}^{t}a(s),ds$, $tin mathbb{R}$, the $N$-function generated by $a$. Let $Omega $ be a bounded open subset of $mathbb{R}^{N}$, $Ngeq 2$, $T[u,u]$ a nonnegative quadratic form involving the only generalized derivatives of order $m$ of the function $uin W_{0}^{m}E_{A}(Omega )$ and $g_{alpha }:Omega imesmathbb{R} omathbb{R}$, $| alpha | Keywords A priori estimate --- critical points --- Orlicz-Sobolev spaces --- Leray-Schauder topological degree --- Duality mapping --- Nemytskij operator --- Mountain Pass Theorem
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