87 research outputs found
A priori bounds for some classes of elliptic equations
No full textWe present an overview on some recent results concerning certain a
priori bounds for the solutions of dfferent kinds of Dirichlet problems for
second order linear elliptic partial differential equations.
We start considering equations in divergence form with discontinuous
coeffcients in unbounded domains. The main theorem, in this case,
consists in a Lp-a priori bound, p > 1 (see [1, 2, 3]).
Applications of this bound in the framework of non variational problems,
in weighted and no-weigthed cases, are also given (cfr. [4, 5]).
Successively, we show some a priori estimates for non-divergence struc-
ture elliptic equations, whose smooth coeffcients satisfy a new condition
generalizing Cordes' one, proved in [6, 7]. The bounds are achieved by
means of a potential estimate obtained for the solutions of the same kind
of problems, but with more regular datum.
References
[1] S. Monsurro, M. Transirico: A Lpestimate for weak solutions of
elliptic equations, Abstr. Appl. Anal. vol. 2012 (2012), 15 pages.
[2] S. Monsurro, M. Transirico: Dirichlet problem for divergence form
elliptic equations with discontinuous coecients, Bound. Value
Probl. vol. 2012 (2012), 20 pages.
[3] S. Monsurro, M. Transirico: A priori bounds in Lp for solutions of
elliptic equations in divergence form, Bull. Sci. Math. 137 (2013),
851-866.
[4] S. Monsurro, M. Transirico: A W2;p-estimate for a class of elliptic
operators, Int. J. Pure Appl. Math. (4) 83 (2013), 489-499
Symmetrization in a nonlinear degenerate parabolic problem
No full textBounds for the solution of a nonlinear degenerate parabolic problem are given by means of the sollution of a "symmetrized" problem
A priori bounds in Lp for solutions of elliptic equations in divergence form
No full textWe prove an a priori bound in Lp, p>1, for the solutions of the Dirichlet problem for second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains
On a potential estimates approach to elliptic equations and its application to a priori estimates
No full textSome remarks on a class of weight functions
No full textsummary:In this paper we obtain some results about a class of functions , where is an open set of , which are related to the distance function from a fixed subset . We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function
Some remarks on the Dirichlet problem for an elliptic equation
No full textThe best constant for the inequality (3) is given; we deduce some results about the Dirichlet problem for an elliptic equation
The Dirichlet problem for elliptic equations in weighted Sobolev spaces
No full textIn this paper we prove some existence and uniqueness results for the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces
The Dirichlet problem for elliptic equations in the plane
No full textsummary:In this paper an existence and uniqueness theorem for the Dirichlet problem in for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class {\it VMO\/}
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
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