Results 181 to 190 of about 1,238 (226)

Opportunities and challenges of diffusion models for generative AI. [PDF]

Natl Sci Rev
Chen M, Mei S, Fan J, Wang M.
europepmc   +1 more source

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows. [PDF]

Proc Natl Acad Sci U S A, 2010
Carlen EA, Carrillo JA, Loss M.
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Existence of Positive Solutions for Semilinear Elliptic Problems involving Critical Sobolev Exponent in Unbouded Domains(Variational Problems and Related Topics)

, 1998
通徳 石渡
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Wavelet transforms on Gelfand-Shilov spaces and concrete examples. [PDF]

J Inequal Appl, 2017
Fukuda N, Kinoshita T, Yoshino K.
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-Laplacian problems with critical Sobolev exponents

Nonlinear Analysis: Theory, Methods & Applications, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Perera, Kanishka, Silva, Elves A. B.
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Quasilinear Elliptic Systems Involving Critical Hardy–Sobolev and Sobolev Exponents

Bulletin of the Malaysian Mathematical Sciences Society, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kang, Dongsheng, Kang, Yangguang
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A quasilinear elliptic problem involving critical Sobolev exponents

Collectanea Mathematica, 2014
The authors study a quasilinear elliptic equation of the form \[ \begin{cases} -\Delta_p u = |u|^{p^*-2}u+g(u), & \text{in } \Omega,\\ u=0, & \text{on }\partial \Omega, \end{cases} \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^N\) with smooth boundary \(\partial\Omega\), \(1 < p < N\), \(\Delta_p\) is the \(p\)-Laplace operator, that is ...
FARACI, FRANCESCA, FARKAS Cs
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The critical Sobolev exponent in two dimensions

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988
SynopsisThe object of the paper is to investigate solutions of equations of the formwithand in particular to look at the asymptotic behaviour of these solutions as γ ↑∞. It is found that, if tγ is the first zero of ϑ, thenwhile tγ is bounded below if p < 2.
McLeod, Bryce, McLeod, Kevin
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Generalized Lyapunov inequalities involving critical Sobolev exponents

Siberian Mathematical Journal, 2012
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Kwon, H. J., Timoshin, S. A.
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The Critical Exponent for Weighted Sobolev Imbeddings

Acta Applicandae Mathematica, 2001
The critical exponent \(p^*\) is defined for the Hardy inequality \[ \Biggl(\int^R_0|u(r)|^q Q(r) dr\Biggr)^{1/q}\leq C\Biggl(\int^R_0|u'(r)|^p P(r) dr\Biggr)^{1/p},\tag{2.5} \] defining an imbedding from a weighted Sobolev space \(V\) with weight \(P(r)\) into the weighted Lebesgue space \(L^q(0,R;Q)\) with weight \(Q(r)\), and it is shown that this ...
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