Litcius/Paper detail

Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group

Patrizia Pucci, Letizia Temperini

2021Advances in Calculus of Variations15 citationsDOI

Abstract

Abstract The paper deals with the existence of nontrivial solutions for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>p</m:mi><m:mo>,</m:mo><m:mi>Q</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math> (p,Q) equations in the Heisenberg group <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="double-struck">H</m:mi><m:mi>n</m:mi></m:msup></m:math> \mathbb{H}^{n} with critical exponential growth at infinity and a singular behavior at the origin. The main features and novelty of the paper are the above generality on the right-hand side of the equation, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>p</m:mi><m:mo>,</m:mo><m:mi>Q</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math> (p,Q) growth of the elliptic operator and the fact that the equation is studied in the entire Heisenberg group.

Topics & Concepts

Heisenberg groupMathematicsGroup (periodic table)Operator (biology)Exponential functionCombinatoricsPhysicsPure mathematicsMathematical analysisQuantum mechanicsTranscription factorGeneChemistryRepressorBiochemistryNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis