Perturbation of a biharmonic eigenvalue problem
Radial limits of the Poisson kernel on the classical Cartan domains
Smale's Conjecture on Mean Values of Polynomials and Electrostatics
2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium...
Some properties of a generalized heat potential (Preliminary communication)
Teoremi di media e formole di maggiorazione relative alle funzioni biarmoniche
The Martin compactification of the polydisc at the bottom of the positive spectrum.
The mean curvature measure
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...
The obstacle problem for the biharmonic operator
Théorie du potentiel associée à certains systèmes différentiels.
Une Variante de L΄Epine De Lebesgue
Uniform bounds for quotients of Green functions on -domains
Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such thatwhere (resp. ) are the Green functions of (resp. ) on .
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Wiener's test of thinness in potential theory
К задаче Коши для уравнения Лапласа с тремя независимыми переменными
О функциях Грина основных краевых задач для уравнения Гельмгольца во внешности компакта
Об исключителных множествах на границе и единственности решений задачи Дирихле для эллиптического уравнения второго порядка
Об устойчивости и единственности решения обратных задач обобщенных потенциалов простого слоя
Принцип Сен-Венана в плоской теории упругости и краевые задачи для бигармонического уравнения в неограниченных областях.
Смешанные обратные задачи теории потенциала в случае звездных тел