{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:04:06Z","timestamp":1787321046784,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>Given $\\alpha \\in [0,2)$ and $f \\in L^2 ((0,T)\\times(0,1))$, we derive new Carleman estimates for the degenerate parabolic problem $w_t + (x^\\alpha w_x) _x =f$, where $(t,x) \\in (0,T) \\times (0,1)$, associated to the boundary conditions $w(t,1)=0$ and $w(t,0)=0$ if $0 \\leq \\alpha &lt;1$ or $(x^\\alpha w_x)(t,0)=0$ if $1\\leq \\alpha &lt;2$. The proof is based on the choice of suitable weighted functions and Hardy-type inequalities. As a consequence, for all $0 \\leq \\alpha &lt;2$ and $\\omega\\subset\\subset(0,1)$, we deduce null controllability results for the degenerate one-dimensional heat equation $u_t - (x^\\alpha u_x)_x = h \\chi _\\omega$ with the same boundary conditions as above.<\/jats:p>","DOI":"10.1137\/04062062x","type":"journal-article","created":{"date-parts":[[2008,1,4]],"date-time":"2008-01-04T18:12:37Z","timestamp":1199470357000},"page":"1-19","source":"Crossref","is-referenced-by-count":178,"title":["Carleman Estimates for a Class of Degenerate Parabolic Operators"],"prefix":"10.1137","volume":"47","author":[{"given":"P.","family":"Cannarsa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Martinez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Vancostenoble","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,1,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-006-0222-6"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2000105"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-002-0746-2"},{"key":"R4","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.57262\/ade\/1355867982","volume":"8","author":"Barbu V.","year":"2003","journal-title":"Adv. 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