... proof of Theorem 3.1.Proof of Theorem 3.1. By elliptic regularity and Lemma 3.2, we haveδ ∈ W2,p1oc() ∩ H10(),and, consequently, the Sobolev embeddingW2,ploc→ C0,n2ploc for p ... 2011:19http://www.advancesindifferenceequations.com/content/2011/1/19Page 7 of 16The regularity of the solution, the Hausdorff dimension and the regularity of the freeboundary are discussed in [2-5]. In [5], on the basis of the monotonicity formula dueto ... AccessPerturbation formula for the two-phasemembrane problemFarid BozorgniaCorrespondence: bozorg@math.ist.utl.ptFaculty of Sciences, Persian GulfUniversity, Bushehr 75168, IranAbstractA perturbation formula...