Partial differential equations

PDE existence, regularity and qualitative results: Cauchy–Kovalevskaya, heat and Airy equations, Euler singularity formation, σ₂ Hessian estimates, radial symmetry, viscosity solutions, Dirichlet and Neumann spectra of the Laplacian.

• Airy equation and Kato smoothing
• Cauchy–Kovalevskaya theorem
• Heat equation
• Hessian estimates for the σ₂ equation
• Pólya's conjecture on Laplacian eigenvalues
• Radial symmetry of semilinear elliptic equations
• Singularity formation for the Euler equations

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