Estimates for the Sobolev trace constant with critical exponent and applications [PDF]
Annali di Matematica Pura ed Applicata, 2007 In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality $S\|u\|^p_{L^{p_*}(\partial ) \hookrightarrow \|u\|^p_{W^{1,p}( )}$ that are independent of $ $. This estimates generalized those of [3] for general $p$.
Nicolas Saintier, J. Fernandez Bonder
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On the Sobolev trace Theorem for variable exponent spaces in the critical range [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2013 21 pages ...
Julián Fernández Bonder +4 more
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Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent [PDF]
Advances in Nonlinear Analysis, 2020 In this article, we consider a class of Kirchhoff equations with critical Hardy-Sobolev exponent and indefinite nonlinearity, which has not been studied in the literature. We prove very nicely that this equation has at least two solutions in ℝ3. And some
Shen Zupei, Yu Jianshe
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Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities [PDF]
Journal of Functional Analysis, 2021 Juncheng Wei, Yuanze Wu
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Critical-exponent Sobolev norms and the Slice Theorem for the quotient space of connections [PDF]
, 2001 The use of certain critical-exponent Sobolev norms is an important feature of methods employed by Taubes to solve the anti-self-dual and similar non-linear elliptic partial differential equations. Indeed, the estimates one can obtain using these critical-
Paul M. N. Feehan
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An existence result for nonlinear elliptic problems involving critical Sobolev exponent [PDF]
, 1985 A. Capozzi +2 more
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Sobolev Critical Exponents of Rational Homotopy Groups [PDF]
Pure and Applied Mathematics Quarterly, 2007 Tristan Rivière
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A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces [PDF]
, 2016 In this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(Ω) for variable exponent Sobolev spaces from the point of view of the Γ-convergence.
Julián Fernández Bonder +2 more
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A system with weights and with critical Sobolev exponent
European Journal of Mathematics, 2023 In this paper, we investigate the minimization problem : $$ \inf_{ \displaystyle{\begin{array}{lll} u \in H_0^1(Ω), v \in H_0^1(Ω),\\ \quad \| u \|_{L^{q}} =1, \quad \| v \|_{L^{q}} = 1 \end{array}}} \left[ \frac{1}{2} \int_Ω a(x) \vert \nabla u(x) \vert^2dx + \displaystyle{ \frac{1}{2} \int_Ω b(x) \vert \nabla v (x)\vert^2dx } - λ\displaystyle{\int_Ω ...
Benhamida, Asma, Hadiji, Rejeb
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On a singular nonlinear Neumann problem [PDF]
Opuscula Mathematica, 2014 We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text ...
Jan Chabrowski
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