EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE

SOBOLEV-HARDY TYPE

Han Junqiang;Wang Yongda;Niu Pengcheng

【期刊名称】《数学物理学报（英文版）》 【年(卷),期】2012(032)005

【摘要】We study the existence of solutions to the following parabolic equation ｛ut-△pu =λ/|x|s|u|q-2 u,(x,t) ∈ Ω × (0,∞),u(x,0) =f(x),x ∈ Ω,(P)u(x,t) =0,(x,t) ∈ δΩ × (0,∞),where-△pu ≡-div(|▽u|p-2 ▽u),1 ＜ p ＜ N,0 ＜ s ≤ p,p≤s≤ q ≤ p*(s) =N-s/N-pp,Ω is a bounded domain in RN such that 0 ∈ Ω with a C1 boundary δΩ,f ≥ 0 satisfying some convenient regularity assumptions.The analysis reveals that the existence of solutions for (P) depends on p,q,s in general,and on the relation between λ and the best constant in the Sobolev-Hardy inequality.

【总页数】18页(1901-1918) 【关键词】

【作者】Han Junqiang;Wang Yongda;Niu Pengcheng

【作者单位】Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China;Department of Applied Mathematics, Northwestern Polytechnical