Pseudodifferential calculus on manifolds with corners and groupoids [PDF]
arXiv, 1997 We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing ...
arxiv
Green Operators in the Edge Calculus [PDF]
arXiv, 2006 The task to construct parametrices of elliptic differential operators on a manifold with edges requires a calculus of operators with a two-component principal symbolic hierarchy, consisting of (edge-degenerate) interior and (operator-valued) edge symbols.
arxiv
Boundary regularity for non-local operators with symmetric kernels and vanishing horizon [PDF]
arXivWe prove optimal H\"older boundary regularity for a non-local operator with a singular, symmetric kernel that depends on the distance to the boundary of the underlying domain. Additionally, we prove higher boundary regularity of solutions.
arxiv
Integral Operators Basic in Random Fields Estimation Theory [PDF]
arXiv, 2004 The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integra$ operator over a bounded domain $\Omega $ in ${\Bbb R}^{n}$ is weakly singular.
arxiv
Non-commutative residue of projections in Boutet de Monvel's calculus [PDF]
arXiv, 2007 Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus.
arxiv
Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains [PDF]
arXiv, 2011 We prove continuity on domains up to the boundary for n/2-polyharmonic maps into manifolds. Technically, we show how to adapt Helein's direct approach to the fractional setting. This extends a remark by the author that this is possible in the setting of Riviere's famous regularity result for critical points of conformally invariant variational ...
arxiv
Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise [PDF]
arXiv, 2012 The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations with nonlocal interactions), asymptotic methods are offered to solve these equations to obtain ...
arxiv
Bifurcation and multiplicity results for critical fractional p-Laplacian problems [PDF]
arXiv, 2014 In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev embedding.
arxiv
Isoperimetric inequalities for Schatten norms of Riesz potentials [PDF]
arXiv, 2015 In this note we prove that the ball is a maximiser of some Schatten $p$-norms of the Riesz potential operators among all domains of a given measure in $\mathbb R^{d}$. In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one ...
arxiv
On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type [PDF]
arXiv, 2015 This paper provides a probabilistic approach to solve linear equations involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we obtain well-posedness results and explicit solutions (in terms of the transition densities of the underlying ...
arxiv