Publications of the Research Institute for Mathematical Sciences
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Weak Solution of a Singular Semilinear Elliptic Equation in a Bounded Domain
We study the singular semilinear elliptic equation
∆u + f(., u) = 0
in
\mathcal D'(Ω)
, where
Ω ⊂ ℝ^n
(
n ≥ 1
) is a bounded domain of class
C^{1,1}. f : Ω × (0, ∞) → [0, ∞)
is such that
f(., u) \in L^1(Ω)
for
u > 0
and
u → f(x, u)
is continuous and nonincreasing for a.e.
x
in
Ω
. We assume that there exists a subset
Ω' ⊂ Ω
with positive measure such that
f(x, u) > 0
for
x\in Ω'
and
u > 0
and that
∫_Ω f(x, cd(x, ∂Ω))dx < ∞
for all
c > 0
. Then we show that there exists a unique solution
u
in
W_0^{1,1}(Ω)
such that
∆u\in L^1(Ω)
,
u > 0
a.e. in
Ω
.
Publications of the Research Institute for Mathematical Sciences - Tập 41 Số 3 - Trang 793-798 - 2005
Solitons and Infinite Dimensional Lie Algebras
Publications of the Research Institute for Mathematical Sciences - Tập 19 Số 3 - Trang 943-1001 - 1983
Global Solutions to the Initial Value Problem for the Nonlinear Boltzmann Equation
Publications of the Research Institute for Mathematical Sciences - Tập 12 Số 1 - Trang 229-239 - 1976
Brundan–Kazhdan–Lusztig and Super Duality Conjectures
Publications of the Research Institute for Mathematical Sciences - Tập 44 Số 4 - Trang 1219-1272 - 2008
The Moduli Space of Extremal Compact Kähler Manifolds and Generalized Well-Petersson Metrics
Publications of the Research Institute for Mathematical Sciences - Tập 26 Số 1 - Trang 101-183 - 1990
Compact Moduli Spaces of Kähler–Einstein Fano Varieties
Publications of the Research Institute for Mathematical Sciences - Tập 51 Số 3 - Trang 549-565 - 2015
The Moduli Space of Kähler Structures on a Real Compact Symplectic Manifold
Publications of the Research Institute for Mathematical Sciences - Tập 24 Số 1 - Trang 141-168 - 1988
Higher Arithmetic $K$-Theory
Publications of the Research Institute for Mathematical Sciences - Tập 41 Số 3 - Trang 599-681 - 2005
A von Neumann Algebra Framework for the Duality of the Quantum Groups
Publications of the Research Institute for Mathematical Sciences - Tập 30 Số 5 - Trang 799-850 - 1994
On the Morawetz–Keel–Smith–Sogge Inequality for the Wave Equation on a Curved Background
Publications of the Research Institute for Mathematical Sciences - Tập 42 Số 3 - Trang 705-720 - 2006
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