Boundedness of weak solutions of degenerate quasilinear equations with\n rough coefficients

2011/06/23 by Dario D. Monticelli, Monticelli, Dario D., Scott Rodney +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1106.4811

Abstract

We derive local boundedness estimates for weak solutions of a large class of\nsecond order quasilinear equations. The structural assumptions imposed on an\nequation in the class allow vanishing of the quadratic form associated with its\nprincipal part and require no smoothness of its coefficients. The class\nincludes second order linear elliptic equations as studied by D. Gilbarg and N.\nS. Trudinger [1998] and second order subelliptic linear equations as studied by\nE. Sawyer and R. L. Wheeden [2006 and 2010]. Our results also extend ones\nobtained by J. Serrin [1964] concerning local boundedness of weak solutions of\nquasilinear elliptic equations.\n

Cited by

• Existence and uniqueness of solutions of degenerate elliptic equations with lower order terms
• Regularizing effects of absorption terms in local-nonlocal mild singular problems

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