A priori inequalities for solutions of mixed boundary-value problems in unbounded domains (Q2505609)

This paper is concerned with the proof of several a priori inequalities for solutions of mixed boundary-value problems for a class of divergence form elliptic equations with discontinuous and unbounded coefficients in bounded or unbounded domains. One of the main purposes is to study the minimal hypotheses on the coefficients and data in order that the associated bilinear form be bounded, even in the case of unbounded domains. The proofs rely on various methods, including elliptic estimates, sub- and super-solutions techniques, Gagliardo type inequalities or Stampacchia regularity results.