Absence of positive eigenvalues for a class of subelliptic operators.
Boundary Behaviour of Nonnegative Solutions of Subelliptic Equations in NTA Domains for Carnot-Carathéodory Metrics.
Asymptotic Behavior of Fundamental Solutions and Potential Theory of Prabolic Operators with Variable Coeeficients.
Carleman estimates for a subelliptic operator and unique continuation
We establish a Carleman type inequality for the subelliptic operator in , , where , . As a consequence, we show that has the strong unique continuation property at points of the degeneracy manifold if the potential is locally in certain spaces.
Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation
A recent result of Bahouri shows that continuation from an open set fails in general for solutions of where and is a (nonelliptic) operator in satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when is the subelliptic Laplacian on the Heisenberg group and is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of to have a finite order...
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.
Trace inequalities for Carnot-Carathéodory spaces and applications
Fatou theorems for some nonlinear elliptic equations.
Comparison theorems for temperatures in noncylindrical domains
In questa Nota gli autori presentano alcuni risultati riguardanti il comportamento alla frontiera di domini non cilindrici delle soluzioni positive dell'equazione del calore. Una conseguenza è che due soluzioni positive qualunque, che si annullano su una parte della frontiera laterale, tendono a zero con lo stesso ordine.
Comparison theorems for temperatures in noncylindrical domains
In questa Nota gli autori presentano alcuni risultati riguardanti il comportamento alla frontiera di domini non cilindrici delle soluzioni positive dell'equazione del calore. Una conseguenza è che due soluzioni positive qualunque, che si annullano su una parte della frontiera laterale, tendono a zero con lo stesso ordine.
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