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An Example of Fractal Singular Homogenization
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Umberto Mosco
Published/Copyright:
March 10, 2010
Abstract
We construct a sequence of quadratic weighted energy forms in an open domain of the plane, that 𝑀-converges to an energy form with a singular fractal term. The weights belong to the Muckenoupt class 𝐴2 and have pointwise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.
Key words and phrases:: Fractal singular homogenization; weighted elliptic operators
Received: 2006-11-09
Published Online: 2010-03-10
Published in Print: 2007-March
© Heldermann Verlag
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Articles in the same Issue
- The Cauchy Transform for the Hodge/De Rham System and Some of its Properties
- Explicit Bounds for Composition Operators Preserving BMO(ℝ)
- A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane
- The Monomiality Approach to Multi-Index Polynomials in Several Variables
- On the Global and Local Solution of the Multidimensional Darboux Problem for Some Nonlinear Wave Equations
- Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
- Generating Relations of Hermite–Tricomi Functions Using a Representation of Lie Algebra 𝑇3
- Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
- An Initial-Boundary Value Problem for a Viscous Compressible Flow
- On the Measurability of Additive Functionals
- On BVPS for Strongly Elliptic Systems with Higher Order Boundary Conditions
- An Example of Fractal Singular Homogenization
- Solution of a Goursat Problem in Optimal Domains
