Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains.

Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains.

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Mihalis Mourgoglou, University of the Basque Country & Ikerbasque
Fine Hall 314

In this talk we will present the extension of the regularity theory of De Giorgi/Nash/Moser for solutions of elliptic PDE in divergence form with merely bounded coefficients in unbounded domains to elliptic operators with lower order terms. The lower order coefficients are assumed to be in some appropriate scale invariant spaces like the Lorentz space with critical exponent or the Stummel-Kato class. An important feature of our results is that all the estimates are scale invariant and independent of the domain, while we do not assume smallness of the norms of the coefficients or coercivity of the associated bilinear form. Time permitting, we will discuss the solution of the variational Dirichlet and obstacle problem, and the construction of the Green’s function à la Grüter and Widman.