25 research outputs found
On some -estimates for solutions of elliptic equations in unbounded domains
No full textsummary:In this review article we present an overview on some a priori estimates in , , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two -bounds, , for the solution of the associated Dirichlet problem, obtained in correspondence with two different sign assumptions. Then, putting together the above mentioned bounds and using a duality argument, we extend the estimate also to the case , for each sign assumption, and for a data in
An Lp-Estimate for Weak Solutions of Elliptic Equations
No full textWe prove an Lp-a priori bound, p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains
Noncoercive nonlinear elliptic equations in unbounded domains
No full text2018 - 2019This research thesis is mainly devoted to the study of noncoercive Dirich let problems with discontinuous coefficients in unbounded domains. The
presence of the noncoercive operator does not allow us to use classical the orems to achieve existence results. Further complications arise as a conse quence of the unboundedness of the domain that yields to the lack of com pactness results. To overcome these difficulties, on one hand we approximate
the solution of the problem by the solutions of suitable coercive nonlinear
Dirichlet problems. On the other hand, we introduce suitable Sobolev spaces
where opportune compactness results hold. [edited by Author]XXXII cicl
Noncoercive elliptic equations with discontinuous coefficients in unbounded domains
No full textIn this paper we study Dirichlet problems for noncoercive linear elliptic equations with discontinuous coefficients in unbounded domains. Exploiting a nonlinear approach, we achieve existence, uniqueness and regularity results
Sobolev inequality with non-uniformly degenerating gradient
No full textIn this paper we prove a weighted Sobolev inequality in a bounded domain Ω ⊂ R^n, n ≥ 1, of a homogeneous space (R^n,ρ,wdx), under suitable compatibility conditions on the positive weight functions (v, w, ω1, ω2, . . . , ωn) and on the quasi-metric ρ
A Priori Bounds in and in for Solutions of Elliptic Equations
No full textWe give an overview on some recent results
concerning the study of the Dirichlet problem for second-order
linear elliptic partial differential equations in divergence form and
with discontinuous coefficients, in unbounded domains. The main
theorem consists in an -a priori bound, . Some applications
of this bound in the framework of non-variational problems, in a
weighted and a non-weighted case, are also given
Uniqueness results for the Dirichlet Problem for higher order elliptic equations in polyhedral angles
No full textWe consider the Dirichlet boundary value problem for higher order elliptic equations in divergence form with discontinuous coefficients in polyhedral angles. Some uniqueness results are proved
POTENTIAL ESTIMATES AND APPLICATIONS TO ELLIPTIC EQUATIONS
No full textIn this paper we prove a potential type estimate for the solutions of some classes of Dirichlet problems associated to certain non divergence structure elliptic equations with smooth datum. As a consequence of our potential bound, we can get an a priori estimate for the solutions of the same kind of Dirichlet problem, but with less regular datum
An application of potential estimates to a priori bounds for elliptic equations
No full textA potential estimate type approach is used in order to obtain
some a priori bounds for the solutions of certain classes of Dirichlet
problems associated to non divergence structure elliptic equations
A W2,p-ESTIMATE FOR A CLASS OF ELLIPTIC OPERATORS
No full textWe prove a W2,p-a priori bound, p > 1, for a class of uniformly elliptic second order differential operators with discontinuous coefficients in un- bounded domains. As an application we obtain the solvability of the related Dirichlet problem
