The Regularity Estimate Of Poission Equation In Orlicz-Sobolev Spaces And Application

Sobolev space and it's promotion play an important role in researching of Par-tial Differential Equations.Orlicz-Sobolev space is a very useful space.It has many characters of Orlicz space and Orlicz-Sobolev space. Orlicz-Sobolev space has im-portant significance to study problems of partial differential equations. Now it has become the focus of people's attention. The regulity of solution of Poission has given in Lp(1<p<+∞) space.The regulity of solution of Poission has not given in Orlicz-Sobolev space.Considering in the reflexive Orlicz space and application the nature of the Orlicz space,this paper gives regularity of Poission by Harmonic Analysis method which use Marcinkiewicz interpolation theorem.Because smooth function is dense in Orlicz space, the Orlicz function can be consistently approximated by smooth function. we proofs existence of solution by smooth function approximation method.The uniqueness of solution of Poission equationcan be proven by coercive congditon. Finally,this paper gives an application in semilinear Poission equation by Schauder fixed point theorem and Orlicz-Sobolev embedded theorem.