| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
This research is concerned with strongly ellptic operators in divergence or non-divergence form under Dirichlet boundary conditions. We showed that the operators are isomorphisms between suitable two Lp Sobolev spaces. Compared with previous studies, this research obtained the same conclusion under much weaker assumptions. As a corollary, we derived a regularity theorem for elliptic equations, which states that the solutions become smoother as the coefficients and the boundary of the domain become smoother. A similar result was also shown in the framework of the Hoelder spaces, which are related to classical differentiability.
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