scholarly journals Magnetostatic Problems in Fractal Domains

2020 ◽  
pp. 477-502
Author(s):  
Simone Creo ◽  
Maria Rosaria Lancia ◽  
Paola Vernole ◽  
Michael Hinz ◽  
Alexander Teplyaev
Keyword(s):  
Fractal Domains

scholarly journals Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains

2010 ◽  
Vol 2010 (1) ◽  
pp. 513186 ◽  
Author(s):  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes ◽  
Paul Bosch
Keyword(s):  
Clifford Algebras ◽  
Extension Theorem ◽  
Fractal Domains

INFINITELY MANY SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPINSKI GASKET

2011 ◽  
Vol 09 (03) ◽  
pp. 235-248 ◽  
Author(s):  
BRIGITTE E. BRECKNER ◽  
VICENŢIU D. RĂDULESCU ◽  
CSABA VARGA
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Dirichlet Boundary ◽  
Sierpinski Gasket ◽  
Infinitely Many Solutions ◽  
Sierpiński Gasket ◽  
Nonlinear Elliptic ◽  
Fractal Domains

We study the nonlinear elliptic equation Δu(x) + a(x)u(x) = g(x)f(u(x)) on the Sierpinski gasket and with zero Dirichlet boundary condition. By extending a method introduced by Faraci and Kristály in the framework of Sobolev spaces to the case of function spaces on fractal domains, we establish the existence of infinitely many weak solutions.

scholarly journals A Hilbert Transform for Matrix Functions on Fractal Domains

2010 ◽  
Vol 6 (2) ◽  
pp. 359-372 ◽  
Author(s):  
R. Abreu-Blaya ◽  
J. Bory-Reyes ◽  
F. Brackx ◽  
H. De Schepper ◽  
F. Sommen
Keyword(s):  
Hilbert Transform ◽  
Matrix Functions ◽  
Fractal Domains

scholarly journals Uniform weighted estimates on pre-fractal domains

2014 ◽  
Vol 19 (7) ◽  
pp. 1969-1985 ◽  
Author(s):  
Raffaela Capitanelli ◽  
◽  
Maria Agostina Vivaldi
Keyword(s):  
Weighted Estimates ◽  
Fractal Domains

scholarly journals Boundary value problems for the Lamé-Navier system in fractal domains

2021 ◽  
Vol 6 (10) ◽  
pp. 10449-10465
Author(s):  
Ricardo Abreu Blaya ◽  
◽  
J. A. Mendez-Bermudez ◽  
Arsenio Moreno García ◽  
José M. Sigarreta ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Representation Formula ◽  
Linear Elasticity Theory ◽  
Fractal Domains

<abstract><p>The aim of this paper is to establish a representation formula for the solutions of the Lamé-Navier system in linear elasticity theory. We also study boundary value problems for such a system in a bounded domain $ \Omega\subset {\mathbb R}^3 $, allowing a very general geometric behavior of its boundary. Our method exploits the connections between this system and some classes of second order partial differential equations arising in Clifford analysis.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document