


Paper's Title:
A Regularity of the Weak Solution Gradient of the Dirichlet Problem for Divergent Form Elliptic Equations in Morrey Spaces
Author(s):
Nicky K. Tumalun and Philotheus E. A. Tuerah
Mathematics Department, Universitas Negeri Manado,
Tondano Selatan, Minahasa Regency,
Sulawesi Utara Province,
Indonesia.
Email: nickytumalun@unima.ac.id,
pheatuerah@unima.ac.id
Abstract:
In this paper we prove that the gradient of the weak solution of the Dirichlet problem for divergent form elliptic equations, with the known term belongs to the Morrey spaces, is the element of the weak Morrey spaces.
Paper's Title:
Some Notes on the Semiopen Subspaces of Topological Spaces
Author(s):
Nicky. K. Tumalun, Philotheus E. A. Tuerah, and Rolles N. S. Palilingan
Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email: nickytumalun@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email: pheatuerah@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Physics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email:
rollespalilingan@unima.ac.id
URL: https://fmipa.unima.ac.id/
Abstract:
In this paper, we obtain some new results regarding to the nowhere dense and first category set in the semiopen subspace of a topological space. More precisely, we prove that a nowhere dense set in the semiopen subspace of a topological space is equivalent as a nowhere dense set in that topological space. This implies that a first category set in the semiopen subspace of a topological space is equivalent as a first category set in that topological space. We also give some applications of these results to give some new proofs relating to the properties of semiopen set and Baire space.
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