1,721,054 research outputs found
Alcuni risultati sulle equazioni di Dirac-Einstein
Full text linkIn this note we introduce the Dirac-Einstein equations on a spin manifold and we review some recent results, in particular: the compactness of the variational solutions, the classification of the Palais-Smale sequences for the related conformal problem, and finally some existence results.In questa nota introduciamo le equazioni di Dirac-Einstein su una varietà spin ed illustriamo alcuni recenti risultati, in particolare: la compattezza delle soluzioni variazionali, la classificazione delle successioni di Palais-Smale per il relativo problema conforme, ed infine alcuni risultati di esistenza
Some integral formulas for the characteristic curvature
No full textWe show some integral formulas involving the characteristic curvature for closed real hypersurfaces in complex spaces
A Smale Type Result and Applications to Contact Homology
Full text linkIn this note we will show that the injection of a suitable subspace of the space of Legendrian loops into the full loop space is an S1-equivariant homotopy equivalence. Moreover, since the smaller space is the space of variations of a given action functional, we will compute the relative Contact Homology of a family of tight contact forms on the three-dimensional torus
Group Actions On The Sphere And Multiplicity Results For The Cr-Yamabe Equation
Full text linkWe will show that the CR-Yamabe equation has several families of infinitely many changing sign solutions, each of them having different symmetries. The problem is variational but it is not Palais-Smale: using different complex group actions on the sphere, we will find many closed subspaces on which we can apply the minmax argument
On the Hopf–Oleinik lemma for degenerate-elliptic equations at characteristic points
No full textIn this paper we discuss the validity of the Hopf lemma at boundary points which are characteristic with respect to certain degenerate-elliptic equations. In the literature there are some positive results under the assumption that the boundary of the domain reflects the underlying geometry of the specific operator. We focus here on conditions on the boundary which are suitable for some families of degenerate operators, also in presence of first order terms
The Rabinowitz–Floer homology for a class of semilinear problems and applications
Full text linkIn this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a starshaped potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model equations
Nonsmooth solutions for a class of fully nonlinear PDE's on Lie groups
No full textIn this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields
Homological approach to problems with jumping non-linearity
No full textIn this paper, we use a perturbed version of the Rabinowitz–Floer homology to find solutions to PDE's with jumping nonlinearities. As applications, we find branches for the Fucik spectrum for the Laplace equation and for systems on manifolds that fiber over S^1
Contact type hypersurfaces and legendre duality
No full textAbstract. In this paper we study contact type hypersurfaces embedded in four-dimensional Kähler manifolds. We are interested whether the so called Legendre duality can be performed and we will show that this can be related to some convexity assumptions, giving a sufficient condition. As an application, in the case of convex hypersurfaces in R4, we will explicitly complete this duality
Characterization of the Palais–Smale sequences for the conformal Dirac–Einstein problem and applications
No full textIn this paper we study the Palais–Smale sequences of the conformal Dirac–Einstein problem. After we characterize the bubbling phenomena, we prove an Aubin type result leading to the existence of a positive solution. Then we show the existence of infinitely many solutions to the problem provided that the underlying manifold exhibits certain symmetries
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