LEADER 05383nam 2200637Ia 450 001 9910462849403321 005 20200520144314.0 010 $a981-4452-33-5 035 $a(CKB)2670000000361841 035 $a(EBL)1193700 035 $a(OCoLC)843871618 035 $a(SSID)ssj0000908118 035 $a(PQKBManifestationID)12361244 035 $a(PQKBTitleCode)TC0000908118 035 $a(PQKBWorkID)10900964 035 $a(PQKB)11061937 035 $a(MiAaPQ)EBC1193700 035 $a(WSP)00002989 035 $a(PPN)189428376 035 $a(Au-PeEL)EBL1193700 035 $a(CaPaEBR)ebr10700619 035 $a(CaONFJC)MIL486891 035 $a(EXLCZ)992670000000361841 100 $a20130419n2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOblique derivative problems for elliptic equations$b[electronic resource] /$fGary M Lieberman 210 $aSingapore $cWorld Scientific$d2013 215 $a1 online resource (528 p.) 300 $aDescription based upon print version of record. 311 $a981-4452-32-7 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. Pointwise Estimates; Introduction; 1.1 The maximum principle; 1.2 The definition of obliqueness; 1.3 The case c < 0, 0 0; 1.4 A generalized change of variables formula; 1.5 The Aleksandrov-Bakel'man-Pucci maximum principles; 1.6 The interior weak Harnack inequality; 1.7 The weak Harnack inequality at the boundary; 1.8 The strong maximum principle and uniqueness; 1.9 Holder continuity; 1.10 The local maximum principle; 1.11 Pointwise estimates for solutions of mixed boundary value problems; 1.12 Derivative bounds for solutions of elliptic equations; Exercises 327 $a2. Classical Schauder Theory from a Modern PerspectiveIntroduction; 2.1 Definitions and properties of Holder spaces; 2.2 An alternative characterization of Holder spaces; 2.3 An existence result; 2.4 Basic interior estimates; 2.5 The Perron process for the Dirichlet problem; 2.6 A model mixed boundary value problem; 2.7 Domains with curved boundary; 2.8 Fredholm-Riesz-Schauder theory; Notes; Exercises; 3. The Miller Barrier and Some Supersolutions for Oblique Derivative Problems; Introduction; 3.1 Theory of ordinary differential equations; 3.2 The Miller barrier construction 327 $a3.3 Construction of supersolutions for Dirichlet data3.4 Construction of a supersolution for oblique derivative problems; 3.5 The strong maximum principle, revisited; 3.6 A Miller barrier for mixed boundary value problems; Notes; Exercises; 4. Holder Estimates for First and Second Derivatives; Introduction; 4.1 C1, estimates for continuous; 4.2 Regularized distance; 4.3 Existence of solutions for continuous; 4.4 Holder gradient estimates for the Dirichlet problem; 4.5 C1, estimates with discontinuous in two dimensions; 4.6 C1, estimates for discontinuous in higher dimensions 327 $a4.7 C2, estimatesNotes; Exercises; 5. Weak Solutions; Introduction; 5.1 Definitions and basic properties of weak derivatives; 5.2 Sobolev imbedding theorems; 5.3 Poincare's inequality; 5.4 The weak maximum principle; 5.5 Trace theorems; 5.6 Existence of weak solutions; 5.7 Higher regularity of solutions; 5.8 Global boundedness of weak solutions; 5.9 The local maximum principle; 5.10 The DeGiorgi class; 5.11 Membership of supersolutions in the De Giorgi class; 5.12 Consequences of the local estimates; 5.13 Integral characterizations of Holder spaces; 5.14 Schauder estimates; Notes; Exercises 327 $a6. Strong SolutionsIntroduction; 6.1 Pointwise estimates for strong solutions; 6.2 A sharp trace theorem; 6.3 Results from harmonic analysis; 6.4 Some further estimates for boundary value problems in a spherical cap; 6.5 Lp estimates for solutions of constant coefficient problems in a spherical cap; 6.6 Local estimates for strong solutions of constant coefficient problems; 6.7 Local interior Lp estimates for the second derivatives of strong solutions of differential equations; 6.8 Local Lp second derivative estimates near the boundary 327 $a6.9 Existence of strong solutions for the oblique derivative problem 330 $aThis book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, no 606 $aDifferential equations, Elliptic 606 $aDifferential equations, Partial 608 $aElectronic books. 615 0$aDifferential equations, Elliptic. 615 0$aDifferential equations, Partial. 676 $a515.3533 700 $aLieberman$b Gary M.$f1952-$057190 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462849403321 996 $aOblique derivative problems for elliptic equations$9255413 997 $aUNINA LEADER 00827nam a2200229 a 4500 001 991003759239707536 008 080701s2007 aa 000 0 alb d 020 $a9789992733899 035 $ab13746959-39ule_inst 040 $aDip.to Lingue$bita 100 1 $aVehbiu, Ardian$0477092 245 10$aFraktalet e shqipes :$bRrėgjimi i gjeometrive tė standardit /$cArdian Vehbiu 260 $aTiranė :$bĒabej,$cc2007 300 $a209 p. ;$c21 cm 440 0$aExcipere ;$vv. 13 650 4$aLingua albanese$xStoria 907 $a.b13746959$b02-04-14$c01-07-08 912 $a991003759239707536 945 $aLE012 491.991 09 VEH$g1$i2012000346628$lle012$o-$pE0.00$q-$rl$s- $t0$u1$v0$w1$x0$y.i14788494$z01-07-08 996 $aFraktalet e shqipes$91226522 997 $aUNISALENTO 998 $ale012$b01-07-08$cm$da $e-$falb$gaa $h0$i0