Class of hypocomplex structures on the two-dimensional torus
Copyright policy )Class of hypocomplex structures on the two-dimensional torus
We study the Hölder solvability of a class of complex vector fields on the torus T 2 \mathbb {T}^2 . We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation L u = a u + b u ¯ Lu=au+b\bar {u} is obtained.
- UNIVERSIDADE DE SAO PAULO Brazil
- Florida International University United States
- Federal University of São Carlos Brazil
similarity principle, Integral representations of solutions to PDEs, first integrals, Existence problems for PDEs: global existence, local existence, non-existence, Linear first-order PDEs, complex vector fields, 35A01, 35C15, 35F05, 58J99, Mathematics - Analysis of PDEs, theta function, FOS: Mathematics, global solvability, Hölder solvability, Cauchy-Pompeiu type integral operator, Analysis of PDEs (math.AP)
similarity principle, Integral representations of solutions to PDEs, first integrals, Existence problems for PDEs: global existence, local existence, non-existence, Linear first-order PDEs, complex vector fields, 35A01, 35C15, 35F05, 58J99, Mathematics - Analysis of PDEs, theta function, FOS: Mathematics, global solvability, Hölder solvability, Cauchy-Pompeiu type integral operator, Analysis of PDEs (math.AP)
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