On the high regularity of solutions to the $$p$$ p -Laplacian boundary value problem in exterior domains

2015 ◽  
Vol 195 (3) ◽  
pp. 821-834 ◽  
Author(s):  
Francesca Crispo ◽  
Carlo Romano Grisanti ◽  
Paolo Maremonti
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Regularity Of Solutions ◽  
Exterior Domains ◽  
High Regularity

scholarly journals An Exterior Neumann Boundary-Value Problem for the Div-Curl System and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1609
Author(s):  
B. Berenice Delgado ◽  
Jorge Eduardo Macías-Díaz
Keyword(s):  
Boundary Value Problem ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Unbounded Domains ◽  
Neumann Boundary ◽  
Explicit Solutions ◽  
Exterior Domains ◽  
Neumann Boundary Value Problem ◽  
Significant Case ◽  
Navier Equation

We investigate a generalization of the equation curlw→=g→ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of Rn using classical operators from Clifford analysis. In the physically significant case n=3, two explicit solutions to the div-curl system in exterior domains of R3 are obtained following different constructions of hyper-conjugate harmonic pairs. One of the constructions hinges on the use of a radial integral operator introduced recently in the literature. An exterior Neumann boundary-value problem is considered for the div-curl system. That system is conveniently reduced to a Neumann boundary-value problem for the Laplace equation in exterior domains. Some results on its uniqueness and regularity are derived. Finally, some applications to the construction of solutions of the inhomogeneous Lamé–Navier equation in bounded and unbounded domains are discussed.

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