%PDF-1.5 % 4 0 obj << /S /GoTo /D (chapter*.1) >> endobj 7 0 obj (Declaration) endobj 8 0 obj << /S /GoTo /D (chapter*.2) >> endobj 11 0 obj (Acknowledgments) endobj 12 0 obj << /S /GoTo /D (chapter*.3) >> endobj 15 0 obj (Dedication) endobj 16 0 obj << /S /GoTo /D (chapter*.4) >> endobj 19 0 obj (Abstract) endobj 20 0 obj << /S /GoTo /D (chapter*.4) >> endobj 22 0 obj (Contents) endobj 23 0 obj << /S /GoTo /D (chapter.1) >> endobj 26 0 obj (Background and Motivations) endobj 27 0 obj << /S /GoTo /D (section.1.1) >> endobj 30 0 obj (Sobolev spaces) endobj 31 0 obj << /S /GoTo /D (section.1.2) >> endobj 34 0 obj (Variational problems) endobj 35 0 obj << /S /GoTo /D (section.1.3) >> endobj 38 0 obj (Literature review) endobj 39 0 obj << /S /GoTo /D (section.1.4) >> endobj 42 0 obj (Integral Calculus of Variations) endobj 43 0 obj << /S /GoTo /D (section.1.5) >> endobj 46 0 obj (Calculus of Variations in L) endobj 47 0 obj << /S /GoTo /D (section.1.6) >> endobj 50 0 obj (Notation convention) endobj 51 0 obj << /S /GoTo /D (section.1.7) >> endobj 54 0 obj (Thesis structure) endobj 55 0 obj << /S /GoTo /D (chapter.2) >> endobj 58 0 obj (Vectorial Variational Problems in L Constrained by the Navier Stokes Equations) endobj 59 0 obj << /S /GoTo /D (section.2.1) >> endobj 62 0 obj (Introduction and main results) endobj 63 0 obj << /S /GoTo /D (section.2.2) >> endobj 66 0 obj (Preliminaries and the main estimates) endobj 67 0 obj << /S /GoTo /D (section.2.3) >> endobj 70 0 obj (Minimisers of Lp problems and convergence as p) endobj 71 0 obj << /S /GoTo /D (section.2.4) >> endobj 74 0 obj (The equations for Lp PDE-constrained minimisers) endobj 75 0 obj << /S /GoTo /D (section.2.5) >> endobj 78 0 obj (The equations for L PDE-constrained minimisers) endobj 79 0 obj << /S /GoTo /D (chapter.3) >> endobj 82 0 obj (On the Isosupremic L Vectorial Minimisation Problem with PDE Constraints) endobj 83 0 obj << /S /GoTo /D (section.3.1) >> endobj 86 0 obj (Introduction and main results) endobj 87 0 obj << /S /GoTo /D (section.3.2) >> endobj 90 0 obj (Minimisers of Lp problems and convergence as p) endobj 91 0 obj << /S /GoTo /D (section.3.3) >> endobj 94 0 obj (The equations for constrained minimisers in Lp and in L) endobj 95 0 obj << /S /GoTo /D (section.3.4) >> endobj 98 0 obj (Explicit classes of nonlinear operators) endobj 99 0 obj << /S /GoTo /D (subsection.3.4.1) >> endobj 102 0 obj (Pointwise constraints, unilateral constraints and inclusions) endobj 103 0 obj << /S /GoTo /D (subsection.3.4.2) >> endobj 106 0 obj (Integral and isoperimetric constraints) endobj 107 0 obj << /S /GoTo /D (subsection.3.4.3) >> endobj 110 0 obj (Quasilinear second order differential constraints) endobj 111 0 obj << /S /GoTo /D (subsection.3.4.4) >> endobj 114 0 obj (Null Lagrangians and determinant constraints) endobj 115 0 obj << /S /GoTo /D (chapter.4) >> endobj 118 0 obj (Generalised Second Order Vectorial -Eigenvalue Problem) endobj 119 0 obj << /S /GoTo /D (section.4.1) >> endobj 122 0 obj (Introduction and main results) endobj 123 0 obj << /S /GoTo /D (section.4.2) >> endobj 126 0 obj (Proofs) endobj 127 0 obj << /S /GoTo /D (chapter.5) >> endobj 130 0 obj (Conclusion and Future Work) endobj 131 0 obj << /S /GoTo /D (section.5.1) >> endobj 134 0 obj (Conclusions) endobj 135 0 obj << /S /GoTo /D (section.5.2) >> endobj 138 0 obj (Future work) endobj 139 0 obj << /S /GoTo /D (appendix.A) >> endobj 142 0 obj (Additional Bound for the Operator Mp) endobj 143 0 obj << /S /GoTo /D (appendix.B) >> endobj 146 0 obj (The Modified H\366lder Inequality) endobj 147 0 obj << /S /GoTo /D (appendix*.9) >> endobj 150 0 obj (Bibliography) endobj 151 0 obj << /S /GoTo /D [152 0 R /FitH] >> endobj 155 0 obj << /Length 486 /Filter /FlateDecode >> stream xڅSn0+xb~:-Z4@ڪ9(mÕ.I)s)|j3]tD},wuqAKFSTaXh$X0=?7Vn7ݦZTÚƧs _P6 #X)&c UXR V2P]ZqE17 Pfh|>5t|DBAB)T1 xy.Rb՘Q) &ƢJ*ˠۨIXk_ DBԬAPzu pr-2]zka^jrA뎓s99V)z)lnHR"qϧHU@Z){B])hĂ0]ׄe*X7zvc5VjU^bq&㦈;7Sݰo‹-k_ͫ7dt@D5[ [&c#fb|M5 5&#W5 FO? 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