... Ω. Then there exists C = C(N,m,λ) (independent of R)such thatinfB(·,R)u ≥ CR−N/λB(·,2R)uλ1/λ. (2.3) The following lemma al lows us to control the parameter τ in the Blow-Up analysis.(See ... to the problem−Δmu = λfx, u+,∇u+−a(x) gu+,∇u+ in Ω,u= 0on∂Ω.(3.6)Multiplying (3.6)byu, integrating over Ω the equation obtained, and applying H¨older’s and Poincare’s ... S1−(θ+1)mnτn.(2.31)Arguing as in the proof of Claim 3 in the above case xn∈ ∂Ω0for all n,wemayassumethat δnSnθ ≥ d0= d0(p, α,β,N,c0) > 0. Therefore, the limit w of the sequence wnsatisfies−Δmw(y)...