Berichtigung zu der Arbeit "Über die Hölderstetigkeit der schwachen Lösungen gewisser semilinearer elliptischer Systeme".
Bernstein and De Giorgi type problems: new results via a geometric approach
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Bernstein approximations of Dirichlet problems for elliptic operators on the plane.
Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Best constant in weighted Sobolev inequality with weights being powers of distance from the origin.
Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain
We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.
"Best possible'' maximum principles
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we prove that the...
Bifurcation and multiplicity results for a nonhomogeneous semilinear elliptic problem.
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Bifurcation for a semilinear elliptic equation on Rn with radially symmetric coefficients.
Bifurcation for Monge-Ampère Equations on Flat Tori.
Bifurcation for nonlinear elliptic boundary value problems I.
This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the...
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Bifurcation from the spectrum towards regular values.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.
Bifurcation of reaction-diffusion systems related to epidemics.
Bifurcation theorems for nonlinear problems with lack of compactness
We deal with a bifurcation result for the Dirichlet problem ⎧ a.e. in Ω, ⎨ ⎩. Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number such that for every the above problem admits a nonzero weak solution in satisfying .
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar...