Results 91 to 100 of about 4,761,041 (315)

Cryogenian Glacial Erosion and Tectonics as Agents of Crustal Recycling

Terra Nova, EarlyView.
ABSTRACT Zircon preserves evidence of recycling processes that link surface environments to the mantle. Combined δ18O‐εHf in zircon fingerprints magmatic sources and tracks how crustal material is reworked over time. We apply statistical analyses to a global compilation that apparently resolves shifts in zircon U–Pb, δ18O, and Lu‐Hf data spanning the ...
M. Seraine, C. J. Spencer, T. M. Gernon, T. Hincks, C. L. Kirkland, E. Rugen, L. DaSilva, H. Shafaii Moghadam, L. P. Soares, G. Fazio   +9 more
wiley   +1 more source

Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity

Mathematics
We consider the minimization of a functional of the calculus of variations, under assumptions that are diffeomorphism invariant. In particular, a nonuniform coercivity condition needs to be considered.
Marco Degiovanni, Marco Marzocchi
doaj   +1 more source

Multiplicity results for logarithmic double phase problems via Morse theory

Bulletin of the London Mathematical Society, EarlyView.
Abstract In this paper, we study elliptic equations of the form −divL(u)=f(x,u)inΩ,u=0on∂Ω,$$\begin{align*} -\operatorname{div}\mathcal {L}(u)=f(x,u)\quad \text{in }\Omega, \quad u=0 \quad \text{on } \partial \Omega, \end{align*}$$where divL$\operatorname{div}\mathcal {L}$ is the logarithmic double phase operator given by div|∇u|p−2∇u+μ(x)|∇u|q(e+|∇u ...
Vicenţiu D. Rădulescu, Matheus F. Stapenhorst, Patrick Winkert   +2 more
wiley   +1 more source

Standing waves of Schrödinger equation with constant magnetic field and combined power nonlinearities

Bulletin of the London Mathematical Society, EarlyView.
Abstract We study standing waves of the Schrödinger equation with constant magnetic field and combined power nonlinearities, which describes a single non‐relativistic quantum particle in the presence of an electromagnetic field. We develop the local minima geometry method to establish the existence, estimates and mass collapse results for this equation,
Zhaosheng Feng, Yu Su
wiley   +1 more source

Sobolev spaces on Lipschitz curves [PDF]

Pacific Journal of Mathematics, 1996
We study Sobolev spaces on a Lipschitz graph \(\Gamma\) by means of a square function involving a geometric second difference. Given a function on the Sobolev space \(W^{1, p}(\Gamma)\) we show that the geometric square function is also in \(L^p(\Gamma)\).
openaire   +4 more sources

The sharp Sobolev type inequalities in the Lorentz–Sobolev spaces in the hyperbolic spaces [PDF]

Journal of Mathematical Analysis and Applications, 2020
Let $W^1L^{p,q}(\mathbb H^n)$, $1\leq q,p < \infty$ denote the Lorentz-Sobolev spaces of order one in the hyperbolic spaces $\mathbb H^n$. Our aim in this paper is three-fold. First of all, we establish a sharp Poincar inequality in $W^1L^{p,q}(\mathbb H^n)$ with $1\leq q \leq p$ which generalizes the result in \cite{NgoNguyenAMV} to the setting ...
openaire   +3 more sources

A fractal local smoothing problem for the wave equation

Bulletin of the London Mathematical Society, EarlyView.
Abstract For any given set E⊂[1,2]$E\subset [1,2]$, we discuss a fractal frequency‐localized version of the Lp$L^p$ local smoothing estimates for the half‐wave propagator with times in E$E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of E$E$ and the Legendre transform.
David Beltran, Joris Roos, Alex Rutar, Andreas Seeger   +3 more
wiley   +1 more source

Traces of Sobolev functions on regular surfaces in infinite dimensions

, 2013
In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O= \{x\in X:\;G(x) 1$, as elements of $L^1(G^{-1}(0), \rho)$ where $\rho$ is the surface measure of Feyel and de ...
Celada, Pietro, Lunardi, Alessandra
core  

Axiomatic theory of Sobolev spaces

Expositiones Mathematicae, 2001
Let \((X,d,\mu)\) be a set \(X\), equipped with a metric \(d\) and a Borel measure \(\mu\). For any \(u\in L^{\text{loc}}_p (X)\), so-called pseudo-gradients \(D[u]\) are introduced axiomatically, and on this basis \(p\)-Dirichlet energies, which, in turn, are used to introduce Sobolev spaces \(W^1_p (X)\).
Marc Troyanov, Vladimir Gol'dshtein
openaire   +3 more sources

Optimal Regularity Properties of the Generalized Sobolev Spaces

Journal of Function Spaces and Applications, 2013
We prove optimal embeddings of the generalized Sobolev spaces , where is a rearrangement invariant function space, into the generalized Hölder-Zygmund space generated by a function space .
G. E. Karadzhov, Qaisar Mehmood
doaj   +1 more source