ar X iv : 0 80 5 . 36 61 v 1 [ m at h . A P ] 2 3 M ay 2 00 8 Boundary singularities of solutions of N - harmonic equations with absorption ∗
نویسنده
چکیده
Abstract We study the boundary behaviour of solutions u of −∆Nu + |u| u = 0 in a bounded smooth domain Ω ⊂ R subject to the boundary condition u = 0 except at one point, in the range q > N − 1. We prove that if q ≥ 2N − 1 such a u is identically zero, while, if N − 1 < q < 2N − 1, u inherits a boundary behaviour which either corresponds to a weak singularity, or to a strong singularity. Such singularities are effectively constructed.
منابع مشابه
ar X iv : 0 80 5 . 37 89 v 1 [ m at h . A P ] 2 4 M ay 2 00 8 The balance between diffusion and absorption in semilinear parabolic equations ∗
Let h : [0,∞) 7→ [0,∞) be continuous and nondecreasing, h(t) > 0 if t > 0, and m,q be positive real numbers. We investigate the behavior when k → ∞ of the fundamental solutions u = uk of ∂tu − ∆u m + h(t)u = 0 in Ω × (0, T ) satisfying uk(x, 0) = kδ0. The main question is wether the limit is still a solution of the above equation with an isolated singularity at (0, 0), or a solution of the asso...
متن کاملar X iv : 0 80 5 . 47 38 v 1 [ he p - th ] 3 0 M ay 2 00 8 U ( 1 ) invariant Membranes and Singularities
A formulation of U(1) symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE’s, as well as some ideas concerning singularities and integrability. Let me start by giving some particular example(s) of a 2-dimensonal (timelike, time periodic) extremal manifold M2 ⊂ R and 3-folds (singularities included) of vanishing mean curvature, in 4...
متن کاملar X iv : 0 81 0 . 06 47 v 1 [ m at h . A P ] 3 O ct 2 00 8 Elliptic Equations Involving Measures ∗
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...
متن کاملar X iv : 0 80 5 . 24 44 v 1 [ m at h . A G ] 1 6 M ay 2 00 8 Symmetry and holomorphy of the second member of the second Painlevé hierarchy
We study symmetry and holomorphy of the second member of the second Painlevé hierarchy P (2) II .
متن کاملar X iv : 0 80 5 . 22 77 v 1 [ m at h . A G ] 1 5 M ay 2 00 8 FUNDAMENTAL GROUPS OF SYMMETRIC SEXTICS . II
We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities 2A8 or A17. We also compute the fundamental groups of a number of other sextics, both of and not of torus type. The groups found are simplest possible, i.e., Z2 ∗Z3 and Z6, respectively.
متن کامل