Results 41 to 50 of about 87,459 (144)
, 2013 We obtain an improved Sobolev inequality in H^s spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmetry of optimizing sequences for the usual Sobolev embedding. More generally,
Palatucci, Giampiero, Pisante, Adriano
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Symmetrization and minimax principles
, 2005 We develop a method to prove that some critical levels for functionals invariant by symmetry obtained by minimax methods without any symmetry constraint are attained by symmetric critical points.
Jean Van Schaftingen
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Concentration-Compactness Principle for embedding into multiple exponential spaces [PDF]
Mathematical Inequalities & Applications, 2012 Let Ω⊂Rn , n 2 , be a bounded domain and let α < n−1 . We prove the ConcentrationCompactness Principle for the embedding of the Orlicz-Sobolev space W 1 0 L n logn−1 L logα logL(Ω) into the Orlicz space corresponding to a Young function that behaves like exp(exp(t n n−1−α )) for large t .
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Equations involving fractional Laplacian operator: Compactness and application
, 2015 In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-\Delta)^{\alpha} u= |u|^{2^*_\alpha-2-\varepsilon}u + \lambda u\,\, {\rm in}\,\, \Omega,\quad u=0 \,\, {\rm on}\, \, \partial\Omega,
Yan, Shusen, Yang, Jianfu, Yu, Xiaohui
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A study and an application of the concentration compactness type principle
, 2019 In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in :p_s^*(x)=(p^+)^*\}$ is nonempty.
Panda, Akasmika, Choudhuri, Debajyoti
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, 2017 We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -{\Delta}u+ u=\big(I_\alpha*|u|^{\frac{\alpha}{N}+1}\big)|u|^{\frac{\alpha}{N}-1}u+f(x,u)\qquad \text{ in ...
Van Schaftingen, Jean, Xia, Jiankang
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Palais-Smale approaches to semilinear elliptic equations in unbounded domains
Electronic Journal of Differential Equations, 2004 Let \(\Omega\) be a domain in \(\mathbb{R}^{N}\), \(N\geq1\), and \(2^{\ast}=\infty\) if \(N=1,2\), \(2^{\ast}=\frac{2N}{N-2}\) if \(N\) is greater than 2, \(2 < p < 2^{\ast}\). Consider the semilinear elliptic problem $$\displaylines{ -\Delta u+u=|u|^{p-
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Lower Semicontinuity of Functionals via the Concentration-Compactness Principle
Journal of Mathematical Analysis and Applications, 2001 AbstractIn this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem.
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Looping dynamics of flexible chain with internal friction at different degree of compactness
, 2015 Recently single molecule experiments have shown the importance of internal friction in biopolymer dynamics. Such studies also suggested that the internal friction although independent of solvent viscosity has strong dependence on denaturant concentration.
Chakrabarti, Rajarshi, Samanta, Nairhita
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Nonlinear stabilitty for steady vortex pairs
, 2012 In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations.
A.L. Mazzucato +25 more
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