Keywords: کلاس کاتو; primary; 35K05; 60J35; 47G20; secondary; 47D07; Heat kernel; Transition density; Non-local operator; Kato class; Lévy system; Gradient estimate;
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Positive solutions with a time-independent boundary singularity of semilinear heat equations in bounded Lipschitz domains
Keywords: کلاس کاتو; primary, 35K91; secondary, 31B10, 35J08, 35J91, 35K08Singular solution; Semilinear heat equation; Semilinear elliptic equation; Heat kernel; Green function; Martin kernel; Kato class
Integrated density of states for Poisson–Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket
Keywords: کلاس کاتو; primary, 60J75, 60H25, 60J35; secondary, 47D08, 28A80Subordinate Brownian motion; Sierpiński gasket; Reflected process; Random Feynman–Kac semigroup; Schrödinger operator; Random potential; Kato class; Eigenvalues; Integrated density of states
Heat kernel estimates for Δ+Δα/2Δ+Δα/2 under gradient perturbation
Keywords: کلاس کاتو; primary, 60J35, 60H10, 35K08; secondary, 47G20, 47D07Heat kernel; Transition density; Feller semigroup; Perturbation; Positivity; Lévy system; Kato class
On minimal support properties of solutions of Schrödinger equations
Keywords: کلاس کاتو; Schrödinger equations; Fefferman-Phong class; Kato class;
Combined effects in a semilinear polyharmonic problem in the unit ball
Keywords: کلاس کاتو; Kato class; positive solution; nonlinear polyharmonic equation; asymptotic behavior; schauder fixed point theorem
Removable singularities and singular solutions of semilinear elliptic equations
Keywords: کلاس کاتو; primary, 35J61; secondary, 31B05, 31B10, 35A01, 35B60Removable singularity; Singular solution; Semilinear elliptic equation; Potential estimate; Iteration method; Kato class; Fixed point argument
On a semilinear fractional Dirichlet problem on a bounded domain
Keywords: کلاس کاتو; Subordinate killed B.M; Fractional power of the negative Dirichlet Laplacian; Green function; Kato class; Dirichlet problem; Positive solution
Asymptotic behavior of positive solutions of a semilinear polyharmonic problem in the unit ball
Keywords: کلاس کاتو; 34B27; 35J40; 35B40; Green function; Kato class; Positive solution; Nonlinear polyharmonic equation; Asymptotic behavior; Schauder fixed point theorem;
A survey of elliptic Kato classes and some applications for partial differential equations
Keywords: کلاس کاتو; Green function; Kato class; 3G-theorem; Dirichlet singular elliptic problem; Asymptotic behavior
Global solutions for a nonlinear absorption parabolic problem in exterior domains
Keywords: کلاس کاتو; 34B27Positive solutions; Green function; Gauss semigroup; Kato class
On dual processes of non-symmetric diffusions with measure-valued drifts
Keywords: کلاس کاتو; primary, 58C60, 60J45; secondary, 35P15, 60G51, 31C25Diffusion; Diffusion process; Non-symmetric diffusion; Dual process; Brownian motion; Kato class; Measure-valued drift; Transition density; Green function; Boundary Harnack principle; Martin boundary; H
On estimates of the density of Feynman–Kac semigroups of α-stable-like processes
Keywords: کلاس کاتو; α-Stable-like processes; Nonsymmetric; Kato class; Feynman–Kac semigroups; Discontinuous additive functionals
On the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearities
Keywords: کلاس کاتو; 31C05; 34B18; 35P30; Nonlinear eigenvalue; Eigenfunction; Green function; Kato class; Superharmonic function; Subsolution; Supersolution;