There Are Thin Minimizers of the <i>L<sup>1</sup>TV</i> Functional

<table>Example of the boundary of a possible minimizer <svg height="10.475" id="M49" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.875 10.475" width="9.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Σ</tspan>
</text>
</g>
</g>
</svg> that does not meet <svg height="10.6875" id="M50" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
</text>
</g>
</g>
</svg> tangentially and illustration of a ball of radius <svg height="11.8" id="M51" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 57.462502 11.8" width="57.462502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.8)">
<g transform="translate(72,-62.56)">
<text transform="matrix(1,0,0,-1,-71.95,62.92)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">𝜆</tspan>
<tspan style="font-size: 12.50px; " x="19.954788" y="0">⊂</tspan>
<tspan style="font-size: 12.50px; " x="31.995176" y="0">Ω</tspan>
</text>
<text transform="matrix(1,0,0,-1,-30.65,68.09)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg> that can be used to find a new minimizer, as described in [<a href="/journals/aaa/2012/930978/#B5">3</a>].</table>

Abstract and Applied Analysis

There Are Thin Minimizers of the L¹TV Functional

Figure 1

Abstract and Applied Analysis

There Are Thin Minimizers of the L1TV Functional

Figure 1

There Are Thin Minimizers of the L¹TV Functional