In this paper we study local regularity properties of weak solutions to a class of nonlinear noncoercive elliptic Dirichlet problems with L1 datum. The model example is -Δp(w)+b(x)|Dw|p-1=f(x)inΩ,w=0on∂Ω.Here Ω ⊂ RN is a bounded open subset, N> 1 , - Δ p is the well known p-Laplace operator, 1 < p< N, b is a function in the Lorentz space LN,1(Ω) and f is a function in L1(Ω). We also investigate similar issues for a lower order perturbation of these problems.
Local regularity results to nonlinear elliptic Dirichlet problems with lower order terms / Clemente, F.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 27:1(2020). [10.1007/s00030-019-0613-3]
Local regularity results to nonlinear elliptic Dirichlet problems with lower order terms
Clemente F.
Primo
2020
Abstract
In this paper we study local regularity properties of weak solutions to a class of nonlinear noncoercive elliptic Dirichlet problems with L1 datum. The model example is -Δp(w)+b(x)|Dw|p-1=f(x)inΩ,w=0on∂Ω.Here Ω ⊂ RN is a bounded open subset, N> 1 , - Δ p is the well known p-Laplace operator, 1 < p< N, b is a function in the Lorentz space LN,1(Ω) and f is a function in L1(Ω). We also investigate similar issues for a lower order perturbation of these problems.| File | Dimensione | Formato | |
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Clemente_Local_2020.pdf
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