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Gradient estimate for solutions of nonlinear singular elliptic equations below the duality exponent
Author(s) -
Cirmi G. R.,
D'Asero S.,
Leonardi S.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4609
Subject(s) - mathematics , bounded function , exponent , mathematical analysis , homogeneous , space (punctuation) , nonlinear system , duality (order theory) , open set , geodetic datum , elliptic curve , dirichlet problem , pure mathematics , boundary value problem , combinatorics , physics , philosophy , linguistics , cartography , quantum mechanics , geography
In this paper, we study the homogeneous Dirichlet problem for an elliptic equation whose simplest model is − Δ u + M | D u | 2u θ= f in Ω ,where Ω ⊂ R N , N ≥3 is an open bounded set, θ ∈]0,1[, and f belongs to a suitable Morrey space. We will show that the Morrey property of the datum is transmitted to the gradient of a solution.