On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method

<div>Transport of <svg height="8.85534pt" id="M213" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.80553 10.1211 8.85534" width="10.1211pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M727 145L694 147C669 79 660 74 614 74H536C582 128 696 227 696 364C696 547 564 666 388 666C215 666 78 544 78 361C78 224 189 126 240 74H155C117 74 102 83 79 147L48 145L64 0H313L320 21C290 72 182 208 182 360C182 527 261 628 387 628S593 523 593 362C593 199 488 69 456 21L461 0H709L727 145Z" id="g50-153"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="768" vert-adv-y="768"></glyph.data></g></svg> after two deformations.</div>

International Journal of Differential Equations

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Figure 3

Figure 3: On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method 