In this paper we focus on the following problem with nonlinear convection term {-div(M(x)∇u)=-div(u|u|θ-1E(x))+f(x)inΩ,u(x)=0on∂Ω,where Ω is an open bounded domain of RN, with N≥ 3 , M(x) is a uniform elliptic matrix with measurable entries, θ∈ (0 , 1) , E(x)∈(Lr(Ω))N, with r∈ (2 , N) , and f(x) ∈ Lm(Ω) , with m> 1. In particular we study how the relation between the parameters θ and r affects existence and summability of solutions.
A nonlinear homotopy between two linear Dirichlet problems / Boccardo, L.; Buccheri, S.. - In: REVISTA MATEMÁTICA COMPLUTENSE. - ISSN 1139-1138. - 34:2(2021), pp. 541-558. [10.1007/s13163-020-00363-x]
A nonlinear homotopy between two linear Dirichlet problems
Boccardo L.;Buccheri S.
2021
Abstract
In this paper we focus on the following problem with nonlinear convection term {-div(M(x)∇u)=-div(u|u|θ-1E(x))+f(x)inΩ,u(x)=0on∂Ω,where Ω is an open bounded domain of RN, with N≥ 3 , M(x) is a uniform elliptic matrix with measurable entries, θ∈ (0 , 1) , E(x)∈(Lr(Ω))N, with r∈ (2 , N) , and f(x) ∈ Lm(Ω) , with m> 1. In particular we study how the relation between the parameters θ and r affects existence and summability of solutions.File in questo prodotto:
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