000			03257cam a2200505 i 4500
003			CUTN
005			20231215153943.0
008			220327s2022 riu b 000 0 eng
020			_a9781470450533
020			_z9781470470159
022			_a00659266
022			_a19476221
041			_aEnglish
042			_apcc
082	0	0	_a515.353 _223/eng20220503 _bGRO
084			_a35K58 _a35K65 _a70S15 _a35K51 _a58J35 _2msc
100	1		_aGross, Leonard,
100	1		_d1931- _eauthor.
245	1	4	_aThe Yang-Mills heat equation with finite action in three dimensions / _cLeonard Gross.
260			_aUSA : _bAmerican Mathematical Society, _cc2022.
300			_av, 111 pages ; _c26 cm
440			_vV.275., No.1349.
490	0		_aMemoirs of the American Mathematical Society, _x0065-9266 ; _vnumber 1349
500			_a"January 2022, volume 275."
504			_aIncludes bibliographical references.
505	0		_aStatement of results -- Solutions for the augmented Yang-Mills heat equation -- Initial behavior of solutions to the augmented equation -- Gauge groups -- The conversion group -- Recovery of A from C.
520			_a"The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R3 and over a bounded open convex set in R3. The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation"--
650		0	_aHeat equation.
650		0	_aYang-Mills theory.
650		0	_aGauge fields (Physics)
650		7	_aPartial differential equations -- Parabolic equations and systems -- Semilinear parabolic equations.
650		7	_aPartial differential equations -- Parabolic equations and systems -- Degenerate parabolic equations.
650		7	_aMechanics of particles and systems -- Classical field theories -- Yang-Mills and other gauge theories.
650		7	_aPartial differential equations -- Parabolic equations and systems -- Initial-boundary value problems for second-order parabolic systems.
650		7	_aGlobal analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods.
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
650		7	_2msc _94
690			_aMathematics
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cPROJECT
999			_c40980 _d40980