02322nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003400207245012100241260008200362300003400444336002600478337002600504338003600530347002400566490004000590506006600630520107800696650003501774650004001809650002601849856003201875856006501907236-180910CH-001817-320180910233004.0a fot ||| 0|cr nn mmmmamaa180910e20180930sz fot ||| 0|eng d a978303719690870a10.4171/1902doi ach0018173 7aPBKJ2bicssc a35-xxa31-xx2msc1 aMaz'ya, Vladimir G.,eauthor.10aBoundary Behavior of Solutions to Elliptic Equations in General Domainsh[electronic resource] /cVladimir G. Maz'ya3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (441 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v301 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present book is a detailed exposition of the author and his collaborators’ work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as “piecewise smoothness” or being a “Lipschitz graph”. The description of the boundary behavior of such solutions is one of the most difficult problems in the theory of partial differential equations. After the famous Wiener test, the main contributions to this area were made by the author. In particular, necessary and sufficient conditions for the validity of imbedding theorems are given, which provide criteria for the unique solvability of boundary value problems of second and higher order elliptic equations. Another striking result is a test for the regularity of a boundary point for polyharmonic equations.
The book will be interesting and useful for a wide audience. It is intended for specialists and graduate students working in the theory of partial differential equations.07aDifferential equations2bicssc07aPartial differential equations2msc07aPotential theory2msc40uhttps://doi.org/10.4171/190423cover imageuhttps://www.ems-ph.org/img/books/mazya_mini.jpg