Nonhomogeneous multiparameter problems in Orlicz–Sobolev spaces
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DOI: 10.1002/mana.202100377
Abstract: This paper is concerned with the existence and multiplicity of solutions for a class of problems involving the Φ‐Laplacian operator with general assumptions on the nonlinearities, which include both semipositone cases and critical concave convex… read more here.
Keywords: problems orlicz; nonhomogeneous multiparameter; sobolev spaces; orlicz sobolev ... See more keywords
The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
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DOI: 10.1007/s00013-021-01594-0
Abstract: We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of… read more here.
Keywords: spaces partial; fractional sobolev; condition; problem fractional ... See more keywords
Characterization of $$H^1$$H1 Sobolev Spaces by Square Functions of Marcinkiewicz Type
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DOI: 10.1007/s00041-018-9618-2
Abstract: We establish characterization of $$H^1$$H1 Sobolev spaces by certain square functions of Marcinkiewicz type. The square functions are related to the Lusin area integrals. Also, in the one dimensional case, the non-periodic version of the… read more here.
Keywords: marcinkiewicz type; characterization sobolev; sobolev spaces; square functions ... See more keywords
On Derivatives, Riesz Transforms and Sobolev Spaces for Fourier–Bessel expansions
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DOI: 10.1007/s00041-021-09896-1
Abstract: We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary derivative. Then we… read more here.
Keywords: derivatives riesz; fourier bessel; bessel expansions; sobolev spaces ... See more keywords
On scales of Sobolev spaces associated to generalized Hardy operators
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DOI: 10.1007/s00209-020-02651-0
Abstract: We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a Hormander multiplier theorem… read more here.
Keywords: associated generalized; hardy; spaces associated; scales sobolev ... See more keywords
Numerical Performance of Optimized Frolov Lattices in Tensor Product Reproducing Kernel Sobolev Spaces
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DOI: 10.1007/s10208-020-09463-y
Abstract: In this paper, we deal with several aspects of the universal Frolov cubature method, which is known to achieve optimal asymptotic convergence rates in a broad range of function spaces. Even though every admissible lattice… read more here.
Keywords: optimized frolov; lattices tensor; numerical performance; performance optimized ... See more keywords
Gossez's approximation theorems in Musielak–Orlicz–Sobolev spaces
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DOI: 10.1016/j.jfa.2018.05.015
Abstract: We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity assumption on $M$… read more here.
Keywords: orlicz sobolev; gossez approximation; musielak orlicz; sobolev spaces ... See more keywords
On Lipschitz approximations in second order Sobolev spaces and the change of variables formula
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DOI: 10.1016/j.jmaa.2021.125659
Abstract: In this paper we study approximations of functions of Sobolev spaces $W^2_{p,\loc}(\Omega)$, $\Omega\subset\mathbb R^n$, by Lipschitz continuous functions. We prove that if $f\in W^2_{p,\loc}(\Omega)$, $1\leq p read more here.
Keywords: loc omega; lipschitz approximations; sobolev spaces; variables formula ... See more keywords
FRACTIONAL FOCK–SOBOLEV SPACES
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DOI: 10.1017/nmj.2018.11
Abstract: Let $s\in \mathbb{R}$ and $0 read more here.
Keywords: spaces mathscr; fractional fock; fock; fock sobolev ... See more keywords
Time Fractional Parabolic Equations with Measurable Coefficients and Embeddings for Fractional Parabolic Sobolev Spaces
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DOI: 10.1093/imrn/rnab229
Abstract: We consider time fractional parabolic equations in divergence and non-divergence form when the leading coefficients $a^{ij}$ are measurable functions of $(t,x_1)$ except for $a^{11}$, which is a measurable function of either $t$ or $x_1$. We… read more here.
Keywords: embeddings fractional; time fractional; fractional parabolic; sobolev spaces ... See more keywords