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This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs.
Related publications (10)
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We establish symmetry results for two categories of overdetermined obstacle problems: Serrin-type problems and problems for two-phase conductors under the overdetermination that the interface serves as a level surface of the solution. The first proof avoid ...
We consider a conservation law with strictly positive wave velocity and study the well-posedness of a suitable notion of solution for the associated initial value problem under a flux constraint active in the half-line R+. The strict positivity of the wave ...
The fractional Caffarelli-Kohn-Nirenberg inequality states that ˆRn ˆRn (u(x) − u(y)) 2 |x| α |x − y| n+2s |y| α dx dy ≥ n,s,p,α,β u|x| −β 2 L p , for 0 < s < min{1, n/2}, 2 < p < 2 * s , and α, β ∈ R so that β − α = s − n 1 2 − 1 p and −2s < α < n−2s 2. C ...