Do you want to publish a course? Click here

Fredholm Properties of Elliptic Operators on $R^n$

128   0   0.0 ( 0 )
 Added by Daniel M. Elton
 Publication date 2000
  fields
and research's language is English




Ask ChatGPT about the research

We study the Fredholm properties of a general class of elliptic differential operators on $R^n$. These results are expressed in terms of a class of weighted function spaces, which can be locally modeled on a wide variety of standard function spaces, and a related spectral pencil problem on the sphere, which is defined in terms of the asymptotic behaviour of the coefficients of the original operator.



rate research

Read More

We study the generalized eigenvalue problem in $mathbb{R}^N$ for a general convex nonlinear elliptic operator which is locally elliptic and positively $1$-homogeneous. Generalizing article of Berestycki and Rossi in [Comm. Pure Appl. Math. 68 (2015), no. 6, 1014-1065] we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.
172 - S.A. Marano , G. Marino , 2018
The existence of positive weak solutions to a singular quasilinear elliptic system in the whole space is established via suitable a priori estimates and Schauders fixed point theorem.
182 - B. Farkas , L. Lorenzi 2008
We consider a class of non-trivial perturbations ${mathscr A}$ of the degenerate Ornstein-Uhlenbeck operator in ${mathbb R}^N$. In fact we perturb both the diffusion and the drift part of the operator (say $Q$ and $B$) allowing the diffusion part to be unbounded in ${mathbb R}^N$. Assuming that the kernel of the matrix $Q(x)$ is invariant with respect to $xin {mathbb R}^N$ and the Kalman rank condition is satisfied at any $xin{mathbb R}^N$ by the same $m<N$, and developing a revised version of Bernsteins method we prove that we can associate a semigroup ${T(t)}$ of bounded operators (in the space of bounded and continuous functions) with the operator ${mathscr A}$. Moreover, we provide several uniform estimates for the spatial derivatives of the semigroup ${T(t)}$ both in isotropic and anisotropic spaces of (Holder-) continuous functions. Finally, we prove Schauder estimates for some elliptic and parabolic problems associated with the operator ${mathscr A}$.
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure and it can even be singular. The first part of the paper presents results concerning the existence of a principal eigenfunction. Then we present various necessary and/or sufficient conditions for the maximum principle to hold, and use these to characterize the simplicity of the principal eigenvalue.
We give necessary and sufficient conditions for the solvability of some semilinear elliptic boundary value problems involving the Laplace operator with linear and nonlinear highest order boundary conditions involving the Laplace-Beltrami operator.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا