Abstract
AbstractIn this paper, we establish the Caccioppoli estimates for the nonlinear differential equation $$ - \overline{D}\bigl( \vert Dv \vert ^{p-2}Dv\bigr) = \lambda \vert v \vert ^{p-2}v, \quad 1< p< \infty ,$$
−
D
‾
(
|
D
v
|
p
−
2
D
v
)
=
λ
|
v
|
p
−
2
v
,
1
<
p
<
∞
,
where D is the Dirac operator. Moreover, we obtain general weighted versions of the Caccioppoli-type inequalities for the Dirac operators.
Funder
Ministry of Education and Science of the Republic of Kazakhstan
Nazarbayev University
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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