NON-LINEAR POTENTIAL THEORY

Abstract

CONTENTSIntroduction Part I § 1. The space § 2. -potentials of generalized functions with finite -energy § 3. The maximum principle. A generalization of a theorem of Evans-Vasilesko. Lemmas on sequences of potentials § 4. The -capacity of a compact set. The capacity potential § 5. The capacity potential of an analytic set. The measurability of an analytic set relative to -capacity and -complete functions § 6. An estimate of the potential in terms of the modulus of continuity of the measure § 7. Metric properties of sets of zero -capacity § 8. Use of Bessel potentials (the case ). The capacity § 9. Guide to the literature Part II § 1. Auxiliary information on the spaces § 2. Generalized functions with finite -energy and -potential § 3. The maximum principle. A generalization of a theorem of Evans-Vasilesko § 4. The -capacity of a compact set. The capacity potential § 5. The capacity potential of an analytic set. Measurability of analytic sets relative to -capacity and -complete functions § 6. An estimate of the potential in terms of the modulus of continuity of the measure § 7. Metric properties of sets of zero -capacity § 8. Use of Bessel potentials (the case ). The capacity References