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LEADER: 02530cam a22003134a 4500
001 5412611
005 20050927121903.0
008 050228s2005 riua b 001 0 eng
010 $a 2005041181
020 $a0821837842 (alk. paper)
035 $a(OCoLC)ocm58423289
035 $a(NNC)5412611
040 $aDLC$cDLC$dYDX$dIXA$dOrLoB-B
042 $apcc
049 $aZCUA
050 00 $aQA379$b.C34 2005
082 00 $a515/.35$222
100 1 $aCaffarelli, Luis A.
245 12 $aA geometric approach to free boundary problems /$cLuis Caffarelli, Sandro Salsa.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$cc2005.
300 $aix, 270 p. :$bill. ;$c27 cm.
440 0 $aGraduate studies in mathematics,$x1065-7339 ;$vv. 68
504 $aIncludes bibliographical references (p. 265-267) and index.
505 00 $gCh. 1.$tAn introductory problem -- $gCh. 2.$tViscosity solutions and their asymptotic developments -- $gCh. 3.$tThe regularity of the free boundary -- $gCh. 4.$tLipschitz free boundaries are C[superscript 1,[gamma]] -- $gCh. 5.$tFlat free boundaries are Lipschitz -- $gCh. 6.$tExistence theory -- $gCh. 7.$tParabolic free boundary problems -- $gCh. 8.$tLipschitz free boundaries : weak results -- $gCh. 9.$tLipschitz free boundaries : strong results -- $gCh. 10.$tFlat free boundaries are smooth -- $gCh. 11.$tBoundary behavior of harmonic functions -- $gCh. 12.$tMonotonicity formulas and applications -- $gCh. 13.$tBoundary behavior of caloric functions.
520 1 $a"Free boundary (or moving boundary or phase transition) problems surface in many areas of analysis, geometry, and applied mathematics. A typical example is the evolving interphase between a solid and liquid phase: if we know the initial configuration well enough, we should be able to reconstruct its evolution, in particular, the evolution of the interphase. In this book we present a series of ideas, methods, and techniques for treating the most basic issues of such a problem. In particular, we describe the very fundamental tools of geometry and real analysis that make this possible: properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity, etc. We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--BOOK JACKET.
650 0 $aBoundary value problems.
650 0 $aLipschitz spaces.
700 1 $aSalsa, S.
852 00 $bmat$hQA379$i.C34 2005