TY - JOUR

T1 - Interior estimates in the sup-norm for a class of generalized functions with integral representations

AU - Ariza, Eusebio

AU - Di Teodoro, Antonio

AU - Vanegas, Judith

N1 - Publisher Copyright:
© 2019, Universidad Simon Bolivar. All rights reserved.

PY - 2019

Y1 - 2019

N2 - In this paper we construct apriori estimates for the first order derivatives in the sup-norm for first order meta-monogenic functions, generalized monogenic functions satisfying a differential equation with an anti-monogenic right hand side and generalized meta-monogenic functions satisfying a differential equation with an anti-meta-monogenic right hand side. We obtain such estimates through integral representations of these classes of functions and give an explicit expression for the corresponding constants appearing in the estimates. Then we show how initial value problems can be solved in case an interior estimate is true in the function spaces under consideration. All related functions are in a Clifford type algebra.

AB - In this paper we construct apriori estimates for the first order derivatives in the sup-norm for first order meta-monogenic functions, generalized monogenic functions satisfying a differential equation with an anti-monogenic right hand side and generalized meta-monogenic functions satisfying a differential equation with an anti-meta-monogenic right hand side. We obtain such estimates through integral representations of these classes of functions and give an explicit expression for the corresponding constants appearing in the estimates. Then we show how initial value problems can be solved in case an interior estimate is true in the function spaces under consideration. All related functions are in a Clifford type algebra.

KW - Clifford type algebras

KW - Initial value problems of Cauchy-Kovaleskaya type

KW - Interior estimates of solutions of elliptic equations

KW - Meta-monogenic functions

UR - http://www.scopus.com/inward/record.url?scp=85074462530&partnerID=8YFLogxK

M3 - Artículo

AN - SCOPUS:85074462530

SN - 2244-8659

VL - 7

SP - 27

EP - 51

JO - Bulletin of Computational Applied Mathematics

JF - Bulletin of Computational Applied Mathematics

IS - 1

ER -