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Harnack's inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients
Dario D. Monticelli, Scott Rodney, Richard L. Wheeden
We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form \begin{eqnarray} \text{div}\big(A(x,u,\na…
A Compact Embedding Theorem for Generalized Sobolev Spaces
Seng-Kee Chua, Scott Rodney, Richard L. Wheeden
We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degen…
Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients
Dario D. Monticelli, Scott Rodney, Richard L. Wheeden
We derive local boundedness estimates for weak solutions of a large class of second order quasilinear equations. The structural assumptions imposed on an equation in the class allo…
Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem
Cristian Rios, Eric Sawyer, Richard Wheeden
In a previous paper we considered a class of infinitely degenerate quasilinear equations and derived a priori bounds for high order derivatives of solutions in terms of the Lipschi…