In this paper we consider a linear elliptic equation in divergence form $$D_j(a_{ij}(x)D_iu) = 0 in Ω.$$ (0.1) Assuming the coefficients a_{ij} in W^{1,n}(Ω) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution u ∈ L^{n′} (Ω) of (0.1) is actually a weak solution in W^{1,2} (Ω).
On the regularity of very weak solutions for linear elliptic equations in divergence form / LA MANNA, DOMENICO ANGELO; Leone, Chiara; Schiattarella, Roberta. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 27:43(2020). [10.1007/s00030-020-00646-8]
On the regularity of very weak solutions for linear elliptic equations in divergence form
Domenico Angelo La Manna;Chiara Leone
;Roberta Schiattarella
2020
Abstract
In this paper we consider a linear elliptic equation in divergence form $$D_j(a_{ij}(x)D_iu) = 0 in Ω.$$ (0.1) Assuming the coefficients a_{ij} in W^{1,n}(Ω) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution u ∈ L^{n′} (Ω) of (0.1) is actually a weak solution in W^{1,2} (Ω).File in questo prodotto:
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