Generalized solutions for a class of non-uniformaly elliptic equations in divergence form |
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Authors: | Gregori Giovanni |
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Institution: | Department Mathematik , ETH Zürich , Zürich, CH-8092, Switzerland |
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Abstract: | We study a general class of quasilinear non-uniformly elliptic pdes in divergence from with linear growth in the gradient. We examine the notions of BV and viscosity solutions and derive for such generalized solutions various a priori pointwise and integral estimates, including a Harnack inequality. In particular we prove that viscosity solutions are unique (on strictly convex domains), are contained in the space BV loc and are C 1,α almost everywhere. |
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