| Abstrakt: |
In this paper, we consider the Dirichlet problem in a bounded open set Ω ⊂ R n ( n ⩾ 2 ) for a class of second-order nonlinear elliptic equations with right-hand side f in L 1 (Ω) . We study the summability of entropy and weak solutions of this problem under the stronger assumption that f G (| f |) ∈ L 1 (Ω) , where G is a nonnegative increasing continuous function on [ 0 , + ∞) . We show how the summability of the solutions depends on the function G. Our conditions on G imply that L 1 + ε (Ω) ⊂ K G ⊂ L 1 (Ω) for every ε > 0 , where K G is the set of all measurable functions v on Ω such that v G (| v |) ∈ L 1 (Ω) . [ABSTRACT FROM AUTHOR] |
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