Results 11 to 20 of about 2,191 (140)
Trace Operators on Regular Trees
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
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
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
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
Spectral Stability of the Neumann Laplacian [PDF]
We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also
Burenkov, V. I., Davies, E. B.
core +2 more sources
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
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
Weighted Sobolev spaces on curves [PDF]
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
Optimality of Serrin type extension criteria to the Navier-Stokes equations
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
Atomic, molecular and wavelet decomposition of generalized 2‐microlocal Besov spaces
We introduce generalized 2‐microlocal Besov spaces and give characterizations in decomposition spaces by atoms, molecules and wavelets. We apply the wavelet decomposition to prove that the 2‐microlocal spaces are invariant under the action of pseudodifferential operators of order 0.
Henning Kempka, Hans Triebel
wiley +1 more source
The concentration-compactness principle for the Trudinger–Moser-type inequality in the Euclidean space was established crucially relying on the Pólya–Szegő inequality which allows to adapt the symmetrization argument.
Li Jungang, Lu Guozhen, Zhu Maochun
doaj +1 more source