Uniqueness For Very Weak Solutions To Boundary Value Problems Of P-harmonic Equation

This paper deals with very weak solutions u∈θ+W01,p-ε(Ω), where to boundary value problems of p-harmonic equationThe main subject is the operator H which carries given function θ into the gradient field Vu. The natural domain of H is the Lebesgue space Lp(Q). We extend the operator H to slightly larger spaces called grand Lp-spaces. Continuity of H is used to prove existence and uniqueness results for homogeneous n-harmonic type equations-divA(x,Vu)=0.