Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 245, Issue 2, Pages 1197-1211Publisher
SPRINGER
DOI: 10.1007/s00205-022-01805-0
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Funding
- RSF [20-11-20272]
- RUDNUniversity Strategic Academic Leadership Program
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This study considers the variational solution to the Zaremba problem for a divergent linear second-order elliptic equation with measurable coefficients. The problem is set in a local Lipschitz graph domain. An estimate in L2+delta, delta > 0, for the gradient of a solution is proved, and an example of the problem with specific Dirichlet data supported by a fractal set of zero (n-1)-dimensional measure and non-zero p-capacity, p > 1, is constructed.
The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+delta, delta > 0, for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n - 1)-dimensional measure and non-zero p-capacity, p > 1 is constructed.
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