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Showing 1 to 2 of 2 for “"Oscillation Estimates"”.
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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… of eigenfunctions, including several crucial estimates for further investigation.</p> <p>(2) Write the nodal set of u as N={u=0}, estimate the size of N using Hausdorff measure. Particularly, surrounding the conjecture that the n-1 dimensional Hausdorff measure is comparable to square root of …
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Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
<p>In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted …