Results 11 to 20 of about 3,977 (146)
Moroccan Journal of Pure and Applied Analysis, 2023 We investigate the existence of non-trivial weak solutions for the following p(x)-Kirchhoff bi-nonlocal elliptic problem driven by both p(x)-Laplacian and p(x)-Biharmonic operators {M(σ)(Δp(x)2u-Δp(x)u)=λϑ(x)|u|q(x)-2u(∫Ωϑ(x)q(x)|u|q(x)dx)r in Ω,u∈W2,p(.)
Jennane Mohsine, Alaoui My Driss Morchid
doaj +1 more source
Sobolev's theorem for double phase functionals
, 2020 Our aim in this paper is to establish generalizations of Sobolev’s theorem for double phase functionals Φ(x,t) = t p + {b(x)t(log(e+ t))τ} , where 1 < p q < ∞ , τ > 0 and b is a nonnegative bounded function satisfying |b(x)− b(y)| C|x− y|θ (log(e+ |x− y|−
Y. Mizuta, T. Ohno, T. Shimomura
semanticscholar +1 more source
Advanced Nonlinear Studies, 2023 Let II be a bounded interval of R{\mathbb{R}} and λ1(I){\lambda }_{1}\left(I) denote the first eigenvalue of the nonlocal operator (−Δ)14{(-\Delta )}^{\tfrac{1}{4}} with the Dirichlet boundary.
Chen Lu, Wang Bohan, Zhu Maochun
doaj +1 more source
Improved Hardy inequalities with exact remainder terms
, 2020 We set up several identities that imply some versions of the Hardy type inequalities. These equalities give a straightforward understanding of several Hardy type inequalities as well as the nonexistence of nontrivial optimizers.
Tuan Duy Nguyen +3 more
semanticscholar +1 more source
Trace Operators on Regular Trees
Analysis and Geometry in Metric Spaces, 2020 We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
Koskela Pekka +2 more
doaj +1 more source
Moroccan Journal of Pure and Applied Analysis, 2021 We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.
Moumni Mostafa El, Mohamed Deval Sidi
doaj +1 more source
Weighted Sobolev spaces on curves [PDF]
, 2002 45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non ...
Pestana, Domingo +3 more
core +3 more sources
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
, 2004 36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this ...
Pestana, Domingo +3 more
core +3 more sources
Optimality of Serrin type extension criteria to the Navier-Stokes equations
Advances in Nonlinear Analysis, 2021 We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
doaj +1 more source
Bilinear weighted Hardy-type inequalities in discrete and q-calculus frameworks
, 2020 We characterize Hardy inequality in weighted Lebesgue sequence spaces involving discrete bilinear Hardy operator ( n ∑ i=−∞ ai )( n ∑ i=−∞ bi ) and then we apply this information to characterize the inequality with q -bilinear Hardy operator Hq( f ,g)(x)
P. Jain +3 more
semanticscholar +1 more source