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1. In t roduct ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Chapter I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2. Liouville theorems I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3. Liouville theorems II . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4. The Harnack inequal i ty . . . . . . . . . . . . . . . . . . . . . . . . . 104 5. Universal a priori es t imates . . . . . . . . . . . . . . . . . . . . . . . 110 Chapte r II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6. A general integral inequali ty I . . . . . . . . . . . . . . . . . . . . . 114 7. A general integral inequali ty II . . . . . . . . . . . . . . . . . . . . . 124 8. Regular i ty theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 9. Historical note: Canchy and Liouville, a quest ion of priori ty . . 138 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities