Geometric maximizers of Schatten norms of some convolution type integral operators [PDF]
, 2017 In this paper we prove that the ball is a maximizer of the Schatten $p$-norm of some convolution type integral operators with non-increasing kernels among all domains of a given measure in $\mathbb R^{d}$.
Ruzhansky, Michael, Suragan, Durvudkhan
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On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group [PDF]
, 2015 In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary".
Ruzhansky, Michael, Suragan, Durvudkhan
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Isoperimetric inequalities for the logarithmic potential operator [PDF]
, 2015 In this paper we prove that the disc is a maximiser of the Schatten $p$-norm of the logarithmic potential operator among all domains of a given measure in $\mathbb R^{2}$, for all even integers $2\leq ...
Ruzhansky, Michael, Suragan, Durvudkhan
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A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [PDF]
, 2017 In this paper we consider the following critical nonlocal problem $$ \left\{\begin{array}{ll} M\left(\displaystyle\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\right)(-\Delta)^s u = \displaystyle\frac{\lambda}{u^\gamma}+u^{2^*_s-1}&\quad ...
Fiscella, Alessio
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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity [PDF]
, 2014 This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical nonlinearity.
Autuori, Giuseppina +2 more
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Multiple solutions of nonlinear equations involving the square root of the Laplacian
, 2017 In this paper we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian $A_{1/2}$ in a smooth bounded domain $\Omega\subset \mathbb{R}^n$ ($n\geq 2$) and with Dirichlet zero-boundary ...
Bisci, Giovanni Molica +2 more
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A Continuous Field of C*-algebras and the Tangent Groupoid for Manifolds with Boundary [PDF]
, 2005 For a smooth manifold with boundary we construct a semigroupoid and a continuous field of C*-algebras which extend Connes' construction of the tangent groupoid.
Aastrup, Johannes +2 more
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A note on semilinear fractional elliptic equation: analysis and discretization [PDF]
, 2016 In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order $s \in (0,1)$. We identify minimal conditions on the nonlinear term and the source which leads to existence of weak ...
Antil, Harbir +2 more
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Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise [PDF]
, 2018 The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered.
Bolin, David +2 more
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Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications [PDF]
, 2018 We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
Antil, Harbir, Rautenberg, Carlos N.
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