In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is -div (a(x, u)Du) = f in D'(Omega) f is an element of L-r (Omega), r > 1, where, for example, a(x, u) = (1 + u)(-theta) with theta is an element of (0, 1). We study the same problem for minima of functionals closely related to the previous equation.
Elliptic equations with degenerate coercivity: Gradient regularity / Giachetti, Daniela; Porzio, Maria Michaela. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - 19:2(2003), pp. 349-370. [10.1007/s10114-002-0235-1]