Author:
Montoro Luigi,Sciunzi Berardino
Abstract
AbstractIn this paper we derive the Pohozaev identity for quasilinear equations $$\begin{aligned} -{\text {div}}(B'(H(\nabla u))\nabla H(\nabla u))=g(x, u) \quad \text{ in }\,\, \Omega , \quad \quad {(E)} \end{aligned}$$
-
div
(
B
′
(
H
(
∇
u
)
)
∇
H
(
∇
u
)
)
=
g
(
x
,
u
)
in
Ω
,
(
E
)
involving the anisotropic Finsler operator $$-{\text {div}}(B'(H(\nabla u))\nabla H(\nabla u))$$
-
div
(
B
′
(
H
(
∇
u
)
)
∇
H
(
∇
u
)
)
. In particular, by means of fine regularity results on the vectorial field $$B'(H(\nabla u))\nabla H(\nabla u)$$
B
′
(
H
(
∇
u
)
)
∇
H
(
∇
u
)
, we prove the identity for weak solutions and in a direct way.
Funder
Università della Calabria
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference16 articles.
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