ar X iv : 0 81 0 . 06 47 v 1 [ m at h . A P ] 3 O ct 2 00 8 Elliptic Equations Involving Measures ∗
نویسنده
چکیده
3 Semilinear equations with absorption 19 3.1 The Marcinkiewicz spaces approach . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Admissible measures and the ∆2-condition . . . . . . . . . . . . . . . . . . . 26 3.3 The duality method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Bessel capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Sharp solvability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 Removable singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4.1 Positive solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4.2 Semilinear elliptic equations with absorption . . . . . . . . . . . . . 40 3.5 Isolated singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.6 The exponential and 2-dimensional cases . . . . . . . . . . . . . . . . . . . . 46 3.6.1 Unconditional solvability . . . . . . . . . . . . . . . . . . . . . . . . 46 3.6.2 Subcritical measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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تاریخ انتشار 2008