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Hocquet, Antoine; Hofmanová, Martina: An energy method for rough partial differential equations. In: JOURNAL OF DIFFERENTIAL EQUATIONS. Jg.265 H. 4. 2018, S. 1407-1466
Inhalt
2. Preliminaries
2.1. Notation
2.2. Unbounded rough drivers
2.3. Assumptions on the coefficients and the main result
3. Analysis of rough partial differential equations
3.1. Rough Gronwall Lemma
3.2. Remainder estimates
4. The energy inequality
4.1. The main statement
4.2. Proof of Proposition 4.1
5. Tensorization
5.1. Preliminary material and main result
5.2. Proof of Proposition 5.1
6. Uniqueness
6.1. Renormalizability of symmetric drivers
6.2. Uniform bound on the drift.
6.3. The proof of uniqueness
7. Existence and stability
Appendix A. Auxiliary results
A.1. Convergence of finite-difference approximations
A.2. The Sewing Lemma
A.3. Families of smoothing operators
References