Titlebook: Geometric Properties for Parabolic and Elliptic PDE‘s; GPPEPDEs, Palinuro, Filippo Gazzola,Kazuhiro Ishige,Paolo Salani Conference proceed

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Symmetry Problems on Stationary Isothermic Surfaces in Euclidean Spaces,Let . be a smooth hypersurface properly embedded in . with . and consider its tubular neighborhood .. We show that, if a heat flow over . with appropriate initial and boundary conditions has . as a stationary isothermic surface, then . must have some sort of symmetry.

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Solvability of a Semilinear Parabolic Equation with Measures as Initial Data,We study a sharp condition for the solvability of the Cauchy problem ., ., where ., . and . is a Radon measure on .. Our results show that the problem does not admit any local nonnegative solutions for some . satisfying . (., .) with a constant .. On the other hand, the problem admits a local solution if . (., .) with a constant ..

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Singular Solutions of the Scalar Field Equation with a Critical Exponent,We consider radially symmetric singular solutions of the scalar field equation with the Sobolev critical exponent. It is shown that there exists a unique special singular solution, and other infinitely many singular solutions are oscillatory around the special singular solution.

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EMI/EMC Computational Modeling Handbookulfills an anisotropic elliptic condition, are established. Such estimates are obtained in terms of solutions to suitable problems with radially symmetric data, when no sign conditions on . are required.

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Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation,s, which are the axisymmetric constant mean curvature surfaces. We consider a linearized stability of these surfaces and derive criteria of the stability by investigating the sign of eigenvalues corresponding to the linearized problem.