1,720,999 research outputs found
LIOUVILLE-TYPE RESULTS FOR THE LANE-EMDEN EQUATION
No full textWe present some Liouville-type result for the Lane-Emden equation in the subcritical and in the critical regimes. In particular, we focus on the so-called critical p−Laplace equation
An overview on extremals and critical points of the Sobolev inequality in convex cones
Full text linkIn this survey, we consider the sharp Sobolev inequality in convex cones. We
also prove it by using the optimal transport technique. Then we present some
results related to the Euler-Lagrange equation of the Sobolev inequality: the
so-called critical p-Laplace equation. Finally, we discuss some stability
results related to the Sobolev inequality
Theory and calibration of HJM with shape factors
No full textWe reconstruct arbitrage free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finite dimensional space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the developement of a historical-implicit hybrid calibration procedure for our infinite-dimensional shape factor model. In this context we also derive a pricing formula for caplets
Uniqueness in Weighted Lebesgue Spaces for an Elliptic Equation with Drift on Manifolds
No full textWe investigate the uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of elliptic equations with a drift posed on a complete, noncompact, Riemannian manifold M of infinite volume and dimension N≥ 2 . Furthermore, in the special case of a model manifold with polynomial volume growth, we show that the conditions on the drift term are sharp
Case-Study: Nonparametric Estimation of Jump-Diffusions
No full textThis case describes and tests a nonparametric procedure introduced in Stanton (1997) in a continuous path setting and then extended to mixed-jump diffusions in Johannes (1999, 2004) and Bandi and Nguyen (1999, 2003), who provide a rigorous treatment of the underlying statistical theory
A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument
Full text linkWe consider the classical ‘‘Serrin's symmetry result” for the overdetermined boundary value problem related to the equation Δu=−1 in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable ‘‘compatibility” assumption between the solution and the geometry of the model
Serrin’s type overdetermined problems in convex cones
Full text linkWe consider overdetermined problems of Serrin’s type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector
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